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1563 lines
79 KiB
C++
1563 lines
79 KiB
C++
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#include "cafHexGridIntersectionTools.h"
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#include "cvfPlane.h"
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#include <cmath>
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#include <algorithm>
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#include <array>
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namespace caf {
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//--------------------------------------------------------------------------------------------------
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///
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//--------------------------------------------------------------------------------------------------
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//HexGridIntersectionTools::ClipVx::ClipVx()
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// : vx(cvf::Vec3d::ZERO),
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// normDistFromEdgeVx1(HUGE_VAL),
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// clippedEdgeVx1Id(-1),
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// clippedEdgeVx2Id(-1),
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// isVxIdsNative(true),
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// derivedVxLevel(-1)
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//{
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//}
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//
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//--------------------------------------------------------------------------------------------------
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/// Find intersection between a line segment and a plane
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///
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/// \param a Start of line segment
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/// \param b End of line segment
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/// \param intersection Returns intersection point along the infinite line defined by a-b
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/// \param normalizedDistFromA Returns the normalized (0..1) position from a to b of the intersection point.
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/// Will return values along the infinite line defined by the a-b direcion,
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/// and HUGE_VAL if plane and line are parallel.
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/// \param epsilon Tolerance margin for accepting the position being within (0..1)
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///
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/// \return True if line segment intersects the plane
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//--------------------------------------------------------------------------------------------------
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bool HexGridIntersectionTools::planeLineIntersect(const cvf::Plane& plane,
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const cvf::Vec3d& a,
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const cvf::Vec3d& b,
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cvf::Vec3d* intersection,
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double* normalizedDistFromA,
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double epsilon)
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{
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// From Real-Time Collision Detection by Christer Eriscon, published by Morgen Kaufmann Publishers, (c) 2005 Elsevier Inc
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cvf::Vec3d ab = b - a;
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cvf::Vec3d normal = plane.normal();
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double normDotAB = normal * ab;
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if (normDotAB == 0)
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{
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(*normalizedDistFromA) = HUGE_VAL;
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return false;
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}
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double interpolationParameter = (-plane.D() - (normal * a)) / normDotAB;
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(*intersection) = a + interpolationParameter * ab;
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(*normalizedDistFromA) = interpolationParameter;
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return (interpolationParameter >= -epsilon && interpolationParameter <= 1.0 + epsilon);
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}
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//--------------------------------------------------------------------------------------------------
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/// Returns whether the triangle was hit by the plane.
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/// isMostVxesOnPositiveSide returns true if all or two of the vxes is on the positive side of the plane.
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/// newVx1/2.vx1ClippedEdge returns the index of the single vx that is alone on one side of the plane.
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/// Going newVx1 to newVx2 will make the top triangle same winding as the original triangle,
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/// and the quad opposite winding
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// The permutations except for the trivial cases where all vertices are in front or behind plane:
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//
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//
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// 1. Single vertex on positive side of plane => isMostVxesOnPositiveSide = false
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//
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// +\ /\3 /\3 /+ /\3 .
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// \ / \ / \ / + / \ + .
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// \2 \ / \/1 __1/____\2__ .
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// / \ \ / /\ / \ .
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// 1/___\1___\2 1/____2/__\2 1/________\2 .
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// +\ /+
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//
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//
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// 2. Two vertices vertex on positive side of plane => isMostVxesOnPositiveSide = true
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//
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// \+ /\3 /\3 +/ /\3 .
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// \ / \ / \ / / \ .
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// \2 \ / \/1 __1/____\2__ .
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// / \ \ / /\ + / \ + .
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// 1/___\1___\2 1/____2/__\2 1/________\2 .
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// \+ +/
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//
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// 3. The special cases of touching one vertex, either exactly or "close enough"
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// in finite precision. These occur for both 2. and 3 and in any rotation.
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//
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// a) Should not be counted b) May need a tolerance margin to intersect
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// as intersecting: both 1->3 and 2->3 as it is theoretically required to:
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// 3
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// \ /\ /|\
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// \ / \ / | \
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// \ / \ / | \
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// \ / \ / | \
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// \/________\ /____|____\
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// \ 1 | 2
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//--------------------------------------------------------------------------------------------------
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bool HexGridIntersectionTools::planeTriangleIntersection(const cvf::Plane& plane,
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const cvf::Vec3d& p1, size_t p1Id,
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const cvf::Vec3d& p2, size_t p2Id,
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const cvf::Vec3d& p3, size_t p3Id,
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ClipVx* newVx1, ClipVx* newVx2,
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bool * isMostVxesOnPositiveSide)
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{
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const double nonDimensionalTolerance = 1.0e-8;
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double sqrSignedDistances[3];
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sqrSignedDistances[0] = plane.distanceSquared(p1);
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sqrSignedDistances[1] = plane.distanceSquared(p2);
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sqrSignedDistances[2] = plane.distanceSquared(p3);
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double maxSqrAbsDistance = std::max(std::abs(sqrSignedDistances[0]),
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std::max(std::abs(sqrSignedDistances[1]),
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std::abs(sqrSignedDistances[2])));
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const double sqrDistanceTolerance = nonDimensionalTolerance * maxSqrAbsDistance;
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int onPosSide[3];
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onPosSide[0] = sqrSignedDistances[0] >= 0;
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onPosSide[1] = sqrSignedDistances[1] >= 0;
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onPosSide[2] = sqrSignedDistances[2] >= 0;
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const int numPositiveVertices = onPosSide[0] + onPosSide[1] + onPosSide[2];
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// The entire triangle is on the negative side
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// Clip everything
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if (numPositiveVertices == 0)
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{
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(*isMostVxesOnPositiveSide) = false;
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return false;
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}
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// All triangle vertices are on the positive side
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if (numPositiveVertices == 3)
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{
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(*isMostVxesOnPositiveSide) = true;
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return false;
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}
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(*isMostVxesOnPositiveSide) = (numPositiveVertices == 2);
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int topVx = 0;
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if (numPositiveVertices == 1)
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{
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if (onPosSide[0]) topVx = 1;
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if (onPosSide[1]) topVx = 2;
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if (onPosSide[2]) topVx = 3;
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// Case 3a: Two negative distances and the last is within tolerance of zero.
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if (sqrSignedDistances[topVx - 1] < sqrDistanceTolerance)
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{
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return false;
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}
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}
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else if (numPositiveVertices == 2)
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{
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if (!onPosSide[0]) topVx = 1;
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if (!onPosSide[1]) topVx = 2;
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if (!onPosSide[2]) topVx = 3;
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// Case 3a: Two positive distances and the last is within tolerance of zero.
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if (sqrSignedDistances[topVx - 1] > -sqrDistanceTolerance)
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{
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return false;
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}
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}
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else
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{
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CVF_ASSERT(false);
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}
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bool ok1 = false;
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bool ok2 = false;
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if (topVx == 1)
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{
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ok1 = planeLineIntersect(plane, p1, p2, &((*newVx1).vx), &((*newVx1).normDistFromEdgeVx1), nonDimensionalTolerance);
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(*newVx1).clippedEdgeVx1Id = p1Id;
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(*newVx1).clippedEdgeVx2Id = p2Id;
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ok2 = planeLineIntersect(plane, p1, p3, &((*newVx2).vx), &((*newVx2).normDistFromEdgeVx1), nonDimensionalTolerance);
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(*newVx2).clippedEdgeVx1Id = p1Id;
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(*newVx2).clippedEdgeVx2Id = p3Id;
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}
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else if (topVx == 2)
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{
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ok1 = planeLineIntersect(plane, p2, p3, &((*newVx1).vx), &((*newVx1).normDistFromEdgeVx1), nonDimensionalTolerance);
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(*newVx1).clippedEdgeVx1Id = p2Id;
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(*newVx1).clippedEdgeVx2Id = p3Id;
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ok2 = planeLineIntersect(plane, p2, p1, &((*newVx2).vx), &((*newVx2).normDistFromEdgeVx1), nonDimensionalTolerance);
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(*newVx2).clippedEdgeVx1Id = p2Id;
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(*newVx2).clippedEdgeVx2Id = p1Id;
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}
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else if (topVx == 3)
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{
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ok1 = planeLineIntersect(plane, p3, p1, &((*newVx1).vx), &((*newVx1).normDistFromEdgeVx1), nonDimensionalTolerance);
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(*newVx1).clippedEdgeVx1Id = p3Id;
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(*newVx1).clippedEdgeVx2Id = p1Id;
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ok2 = planeLineIntersect(plane, p3, p2, &((*newVx2).vx), &((*newVx2).normDistFromEdgeVx1), nonDimensionalTolerance);
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(*newVx2).clippedEdgeVx1Id = p3Id;
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(*newVx2).clippedEdgeVx2Id = p2Id;
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}
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else
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{
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CVF_ASSERT(false);
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}
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//CVF_TIGHT_ASSERT(ok1 && ok2);
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return true;
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}
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//--------------------------------------------------------------------------------------------------
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//
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//
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// P2 P2 P2 P2
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// Keep Keep Keep Keep
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// None Top 3 Quad All
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// | | + | |
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// | | / \ | |
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// | | | | / \ | | | |
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// | | | | / \ | | | |
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// | | | | / \| | | |
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// | | | |/ 1+ | | |
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// | | | +2 |\ | | |
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// | | | /| | \ | | |
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// | | | / | | \ | _ | |
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// | | | / | | \| |\Dir | |
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// | | |/ | | 1+ \ | |
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// | | +2 | | |\ \ | |
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// | | /| | | | \ | |
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// | | / |1 |1 2| 2| \ | |
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// | | +--+----+----------+----+---+ | |
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// | |1 | | | | 2 | |
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// P1 P1 P1 P1
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// Keep Keep Keep Keep
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// All Quad Top None
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//
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//
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// Clips the supplied triangles into new triangles returned in clippedTriangleVxes.
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// New vertices have set isVxIdsNative = false and their vxIds is indices into triangleVxes
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// The cellFaceForEachTriangleEdge refer to the edge after the corresponding triangle vertex.
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// This method will keep the faces provided, while added edges is marked with no face = 6
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//--------------------------------------------------------------------------------------------------
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void HexGridIntersectionTools::clipTrianglesBetweenTwoParallelPlanes(const std::vector<ClipVx>& triangleVxes,
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const std::vector<int>& cellFaceForEachTriangleEdge,
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const cvf::Plane& p1Plane,
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const cvf::Plane& p2Plane,
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std::vector<ClipVx>* clippedTriangleVxes,
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std::vector<int>* cellFaceForEachClippedTriangleEdge)
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{
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#define HT_NO_FACE 6
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size_t triangleCount = triangleVxes.size() / 3;
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for (size_t tIdx = 0; tIdx < triangleCount; ++tIdx)
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{
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size_t triVxIdx = tIdx * 3;
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ClipVx newVx1OnP1;
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newVx1OnP1.isVxIdsNative = false;
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ClipVx newVx2OnP1;
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newVx2OnP1.isVxIdsNative = false;
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bool isMostVxesOnPositiveSideOfP1 = false;
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bool isIntersectingP1 = planeTriangleIntersection(p1Plane,
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triangleVxes[triVxIdx + 0].vx, triVxIdx + 0,
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triangleVxes[triVxIdx + 1].vx, triVxIdx + 1,
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triangleVxes[triVxIdx + 2].vx, triVxIdx + 2,
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&newVx1OnP1, &newVx2OnP1, &isMostVxesOnPositiveSideOfP1);
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if (!isIntersectingP1 && !isMostVxesOnPositiveSideOfP1)
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{
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continue; // Discard triangle
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}
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ClipVx newVx1OnP2;
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newVx1OnP2.isVxIdsNative = false;
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ClipVx newVx2OnP2;
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newVx2OnP2.isVxIdsNative = false;
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bool isMostVxesOnPositiveSideOfP2 = false;
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bool isIntersectingP2 = planeTriangleIntersection(p2Plane,
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triangleVxes[triVxIdx + 0].vx, triVxIdx + 0,
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triangleVxes[triVxIdx + 1].vx, triVxIdx + 1,
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triangleVxes[triVxIdx + 2].vx, triVxIdx + 2,
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&newVx1OnP2, &newVx2OnP2, &isMostVxesOnPositiveSideOfP2);
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if (!isIntersectingP2 && !isMostVxesOnPositiveSideOfP2)
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{
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continue; // Discard triangle
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}
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bool p1KeepAll = (!isIntersectingP1 && isMostVxesOnPositiveSideOfP1);
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bool p2KeepAll = (!isIntersectingP2 && isMostVxesOnPositiveSideOfP2);
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bool p1KeepQuad = ( isIntersectingP1 && isMostVxesOnPositiveSideOfP1);
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bool p2KeepQuad = ( isIntersectingP2 && isMostVxesOnPositiveSideOfP2);
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bool p1KeepTop = ( isIntersectingP1 && !isMostVxesOnPositiveSideOfP1);
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bool p2KeepTop = ( isIntersectingP2 && !isMostVxesOnPositiveSideOfP2);
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if (p1KeepAll && p2KeepAll)
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{
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// Keep the triangle
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clippedTriangleVxes->push_back(triangleVxes[triVxIdx + 0]);
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clippedTriangleVxes->push_back(triangleVxes[triVxIdx + 1]);
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clippedTriangleVxes->push_back(triangleVxes[triVxIdx + 2]);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[triVxIdx + 0]);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[triVxIdx + 1]);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[triVxIdx + 2]);
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continue;
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}
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if (p1KeepQuad && p2KeepAll)
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{
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// Split the resulting quad and add the two triangles
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clippedTriangleVxes->push_back(newVx2OnP1);
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clippedTriangleVxes->push_back(newVx1OnP1);
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clippedTriangleVxes->push_back(triangleVxes[newVx1OnP1.clippedEdgeVx2Id]);
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clippedTriangleVxes->push_back(triangleVxes[newVx1OnP1.clippedEdgeVx2Id]);
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clippedTriangleVxes->push_back(triangleVxes[newVx2OnP1.clippedEdgeVx2Id]);
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clippedTriangleVxes->push_back(newVx2OnP1);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP1.clippedEdgeVx1Id]);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP1.clippedEdgeVx2Id]);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx2OnP1.clippedEdgeVx2Id]);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
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continue;
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}
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if (p2KeepQuad && p1KeepAll)
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{
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// Split the resulting quad and add the two triangles
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clippedTriangleVxes->push_back(newVx2OnP2);
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clippedTriangleVxes->push_back(newVx1OnP2);
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clippedTriangleVxes->push_back(triangleVxes[newVx2OnP2.clippedEdgeVx2Id]);
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clippedTriangleVxes->push_back(newVx1OnP2);
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clippedTriangleVxes->push_back(triangleVxes[newVx1OnP2.clippedEdgeVx2Id]);
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clippedTriangleVxes->push_back(triangleVxes[newVx2OnP2.clippedEdgeVx2Id]);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx2OnP2.clippedEdgeVx2Id]);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP2.clippedEdgeVx1Id]);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP2.clippedEdgeVx2Id]);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
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continue;
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}
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if (p1KeepTop && p2KeepAll)
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{
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// Add the top triangle
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clippedTriangleVxes->push_back(newVx1OnP1);
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clippedTriangleVxes->push_back(newVx2OnP1);
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clippedTriangleVxes->push_back(triangleVxes[newVx1OnP1.clippedEdgeVx1Id]);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx2OnP1.clippedEdgeVx2Id]);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP1.clippedEdgeVx1Id]);
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continue;
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}
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if (p2KeepTop && p1KeepAll)
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{
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// Add the top triangle
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clippedTriangleVxes->push_back(newVx1OnP2);
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clippedTriangleVxes->push_back(newVx2OnP2);
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clippedTriangleVxes->push_back(triangleVxes[newVx1OnP2.clippedEdgeVx1Id]);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx2OnP2.clippedEdgeVx2Id]);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP2.clippedEdgeVx1Id]);
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continue;
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}
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if (p1KeepQuad && p2KeepQuad)
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{
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// We end up with a pentagon.
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clippedTriangleVxes->push_back(newVx2OnP1);
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clippedTriangleVxes->push_back(newVx1OnP1);
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clippedTriangleVxes->push_back(newVx2OnP2);
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clippedTriangleVxes->push_back(newVx2OnP2);
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clippedTriangleVxes->push_back(newVx1OnP2);
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clippedTriangleVxes->push_back(newVx2OnP1);
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// Two variants. The original point might be along newVx1OnP1 to newVx2OnP2 or along newVx2OnP1 to newVx1OnP2
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if (newVx1OnP1.clippedEdgeVx2Id == newVx2OnP2.clippedEdgeVx1Id)
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{
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clippedTriangleVxes->push_back(newVx2OnP1);
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clippedTriangleVxes->push_back(newVx1OnP2);
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clippedTriangleVxes->push_back(triangleVxes[newVx2OnP1.clippedEdgeVx2Id]);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
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cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP1.clippedEdgeVx1Id]);
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cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP2.clippedEdgeVx1Id]);
|
|
cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx2OnP1.clippedEdgeVx2Id]);
|
|
}
|
|
else
|
|
{
|
|
|
|
clippedTriangleVxes->push_back(newVx2OnP2);
|
|
clippedTriangleVxes->push_back(newVx1OnP1);
|
|
clippedTriangleVxes->push_back(triangleVxes[newVx2OnP2.clippedEdgeVx2Id]);
|
|
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP2.clippedEdgeVx1Id]);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP1.clippedEdgeVx1Id]);
|
|
cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx2OnP2.clippedEdgeVx2Id]);
|
|
}
|
|
|
|
continue;
|
|
}
|
|
|
|
if (p1KeepQuad && p2KeepTop)
|
|
{
|
|
// We end up with a quad.
|
|
clippedTriangleVxes->push_back(newVx1OnP1);
|
|
clippedTriangleVxes->push_back(newVx1OnP2);
|
|
clippedTriangleVxes->push_back(newVx2OnP1);
|
|
|
|
clippedTriangleVxes->push_back(newVx1OnP2);
|
|
clippedTriangleVxes->push_back(newVx2OnP2);
|
|
clippedTriangleVxes->push_back(newVx2OnP1);
|
|
|
|
cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP1.clippedEdgeVx1Id]);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx2OnP2.clippedEdgeVx2Id]);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
|
|
continue;
|
|
}
|
|
|
|
if (p2KeepQuad && p1KeepTop)
|
|
{
|
|
// We end up with a quad.
|
|
clippedTriangleVxes->push_back(newVx2OnP1);
|
|
clippedTriangleVxes->push_back(newVx2OnP2);
|
|
clippedTriangleVxes->push_back(newVx1OnP2);
|
|
|
|
clippedTriangleVxes->push_back(newVx2OnP1);
|
|
clippedTriangleVxes->push_back(newVx1OnP2);
|
|
clippedTriangleVxes->push_back(newVx1OnP1);
|
|
|
|
cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx2OnP1.clippedEdgeVx2Id]);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
cellFaceForEachClippedTriangleEdge->push_back(cellFaceForEachTriangleEdge[newVx1OnP2.clippedEdgeVx1Id]);
|
|
cellFaceForEachClippedTriangleEdge->push_back(HT_NO_FACE);
|
|
|
|
continue;
|
|
}
|
|
|
|
CVF_ASSERT(false);
|
|
}
|
|
}
|
|
|
|
//--------------------------------------------------------------------------------------------------
|
|
// Creates a plane with normal perpendicular to the edge, pointing in the direction of the pointInNormalDirection
|
|
//--------------------------------------------------------------------------------------------------
|
|
cvf::Plane createPlaneFromEdgeAndPointInNormalDirection(cvf::Vec3d ep1, cvf::Vec3d ep2, cvf::Vec3d pointInNormalDirection)
|
|
{
|
|
cvf::Vec3d ep1ep2 = ep2 - ep1;
|
|
cvf::Vec3d ep1pointforNorm = pointInNormalDirection - ep1;
|
|
cvf::Vec3d triNormal = ep1ep2^ep1pointforNorm;
|
|
cvf::Vec3d pointInPlane = ep1 + triNormal;
|
|
|
|
cvf::Plane plane;
|
|
plane.setFromPoints(ep1, pointInPlane, ep2);
|
|
|
|
return plane;
|
|
}
|
|
|
|
//--------------------------------------------------------------------------------------------------
|
|
// Clips the supplied triangles into new triangles returned in clippedTriangleVxes.
|
|
// New vertices have set isVxIdsNative = false and their vxIds is indices into triangleVxes
|
|
// The cellFaceForEachTriangleEdge refer to the edge after the corresponding triangle vertex.
|
|
// This method will keep the faces provided, while added edges is marked with no face = 6
|
|
//--------------------------------------------------------------------------------------------------
|
|
void HexGridIntersectionTools::clipPlanarTrianglesWithInPlaneTriangle(const std::vector<cvf::Vec3d>& triangleVxes,
|
|
const std::vector<int>& cellFaceForEachTriangleEdge,
|
|
const cvf::Vec3d& tp1,
|
|
const cvf::Vec3d& tp2,
|
|
const cvf::Vec3d& tp3,
|
|
std::vector<cvf::Vec3d>* clippedTriangleVxes,
|
|
std::vector<int>* cellFaceForEachClippedTriangleEdge)
|
|
{
|
|
#define HT_NO_FACE 6
|
|
|
|
size_t triangleCount = triangleVxes.size() / 3;
|
|
|
|
// Creating a plane for each of the edges of the clipping triangle
|
|
std::array<cvf::Plane, 3> clipTrianglePlanes;
|
|
|
|
clipTrianglePlanes[0] = createPlaneFromEdgeAndPointInNormalDirection ( tp1, tp2, tp3 );
|
|
clipTrianglePlanes[1] = createPlaneFromEdgeAndPointInNormalDirection ( tp2, tp3, tp1 );
|
|
clipTrianglePlanes[2] = createPlaneFromEdgeAndPointInNormalDirection ( tp3, tp1, tp2 );
|
|
|
|
#define reserveSize 100
|
|
|
|
std::vector<cvf::Vec3d> currentInputTriangleVxes;
|
|
currentInputTriangleVxes.reserve(reserveSize);
|
|
std::vector<int> currentInputCellFaceForEachTriangleEdge;
|
|
currentInputCellFaceForEachTriangleEdge.reserve(reserveSize);
|
|
std::vector<cvf::Vec3d> currentOutputTriangleVxes;
|
|
currentOutputTriangleVxes.reserve(reserveSize);
|
|
std::vector<int> currentOutputCellFaceForEachTriangleEdge;
|
|
currentOutputCellFaceForEachTriangleEdge.reserve(reserveSize);
|
|
|
|
for( size_t tIdx = 0; tIdx < triangleCount; ++tIdx )
|
|
{
|
|
size_t triVxIdx = tIdx * 3;
|
|
|
|
currentInputTriangleVxes.clear();
|
|
currentInputCellFaceForEachTriangleEdge.clear();
|
|
currentOutputTriangleVxes.clear();
|
|
currentOutputCellFaceForEachTriangleEdge.clear();
|
|
|
|
currentOutputTriangleVxes.push_back(triangleVxes[triVxIdx + 0]);
|
|
currentOutputTriangleVxes.push_back(triangleVxes[triVxIdx + 1]);
|
|
currentOutputTriangleVxes.push_back(triangleVxes[triVxIdx + 2]);
|
|
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(cellFaceForEachTriangleEdge[triVxIdx + 0]);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(cellFaceForEachTriangleEdge[triVxIdx + 1]);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(cellFaceForEachTriangleEdge[triVxIdx + 2]);
|
|
|
|
ClipVx newVx1;
|
|
newVx1.isVxIdsNative = false;
|
|
ClipVx newVx2;
|
|
newVx2.isVxIdsNative = false;
|
|
|
|
for ( int planeIdx = 0; planeIdx < 3; ++planeIdx )
|
|
{
|
|
currentInputTriangleVxes.swap(currentOutputTriangleVxes);
|
|
currentInputCellFaceForEachTriangleEdge.swap(currentOutputCellFaceForEachTriangleEdge);
|
|
|
|
currentOutputTriangleVxes.clear();
|
|
currentOutputCellFaceForEachTriangleEdge.clear();
|
|
|
|
size_t inTriangleCount = currentInputTriangleVxes.size()/3;
|
|
|
|
for ( size_t inTrIdx = 0; inTrIdx < inTriangleCount ; ++inTrIdx )
|
|
{
|
|
size_t inTriVxIdx = inTrIdx * 3;
|
|
|
|
bool isMostVxesOnPositiveSide = false;
|
|
|
|
bool isIntersectingPlane = planeTriangleIntersection(clipTrianglePlanes[planeIdx],
|
|
currentInputTriangleVxes[inTriVxIdx + 0], inTriVxIdx + 0,
|
|
currentInputTriangleVxes[inTriVxIdx + 1], inTriVxIdx + 1,
|
|
currentInputTriangleVxes[inTriVxIdx + 2], inTriVxIdx + 2,
|
|
&newVx1, &newVx2, &isMostVxesOnPositiveSide);
|
|
|
|
|
|
if ( !isIntersectingPlane)
|
|
{
|
|
// All on negative side: Discard triangle
|
|
|
|
if (!isMostVxesOnPositiveSide)
|
|
{
|
|
continue;
|
|
}
|
|
else // All on positive side: keep all
|
|
{
|
|
currentOutputTriangleVxes.push_back(currentInputTriangleVxes[inTriVxIdx + 0]);
|
|
currentOutputTriangleVxes.push_back(currentInputTriangleVxes[inTriVxIdx + 1]);
|
|
currentOutputTriangleVxes.push_back(currentInputTriangleVxes[inTriVxIdx + 2]);
|
|
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(currentInputCellFaceForEachTriangleEdge[inTriVxIdx + 0]);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(currentInputCellFaceForEachTriangleEdge[inTriVxIdx + 1]);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(currentInputCellFaceForEachTriangleEdge[inTriVxIdx + 2]);
|
|
}
|
|
}
|
|
else // intersecting
|
|
{
|
|
if ( isMostVxesOnPositiveSide )
|
|
{
|
|
// We need the Quad
|
|
|
|
currentOutputTriangleVxes.push_back(newVx2.vx);
|
|
currentOutputTriangleVxes.push_back(newVx1.vx);
|
|
currentOutputTriangleVxes.push_back(currentInputTriangleVxes[newVx1.clippedEdgeVx2Id]);
|
|
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(HT_NO_FACE);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(currentInputCellFaceForEachTriangleEdge[newVx1.clippedEdgeVx1Id]);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(HT_NO_FACE);
|
|
|
|
currentOutputTriangleVxes.push_back(currentInputTriangleVxes[newVx1.clippedEdgeVx2Id]);
|
|
currentOutputTriangleVxes.push_back(currentInputTriangleVxes[newVx2.clippedEdgeVx2Id]);
|
|
currentOutputTriangleVxes.push_back(newVx2.vx);
|
|
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(currentInputCellFaceForEachTriangleEdge[newVx1.clippedEdgeVx2Id]);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(currentInputCellFaceForEachTriangleEdge[newVx2.clippedEdgeVx2Id]);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(HT_NO_FACE);
|
|
}
|
|
else
|
|
{
|
|
currentOutputTriangleVxes.push_back(newVx1.vx);
|
|
currentOutputTriangleVxes.push_back(newVx2.vx);
|
|
currentOutputTriangleVxes.push_back(currentInputTriangleVxes[newVx1.clippedEdgeVx1Id]);
|
|
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(HT_NO_FACE);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(currentInputCellFaceForEachTriangleEdge[newVx2.clippedEdgeVx2Id]);
|
|
currentOutputCellFaceForEachTriangleEdge.push_back(currentInputCellFaceForEachTriangleEdge[newVx1.clippedEdgeVx1Id]);
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
// Append the result of the completely clipped triangle to the output
|
|
|
|
clippedTriangleVxes->insert(clippedTriangleVxes->end(), currentOutputTriangleVxes.begin(), currentOutputTriangleVxes.end());
|
|
cellFaceForEachClippedTriangleEdge->insert(cellFaceForEachClippedTriangleEdge->end(), currentOutputCellFaceForEachTriangleEdge.begin(), currentOutputCellFaceForEachTriangleEdge.end());
|
|
}
|
|
}
|
|
|
|
//--------------------------------------------------------------------------------------------------
|
|
/// Will return the intersection point. If the plane is outside the line, it returns the closest line endpoint
|
|
//--------------------------------------------------------------------------------------------------
|
|
cvf::Vec3d HexGridIntersectionTools::planeLineIntersectionForMC(const cvf::Plane& plane, const cvf::Vec3d& p1, const cvf::Vec3d& p2, double* normalizedDistFromP1)
|
|
{
|
|
// From http://local.wasp.uwa.edu.au/~pbourke/geometry/planeline/
|
|
//
|
|
// P1 (x1,y1,z1) and P2 (x2,y2,z2)
|
|
//
|
|
// P = P1 + u (P2 - P1)
|
|
//
|
|
// A*x1 + B*y1 + C*z1 + D
|
|
// u = ---------------------------------
|
|
// A*(x1-x2) + B*(y1-y2) + C*(z1-z2)
|
|
|
|
CVF_TIGHT_ASSERT(normalizedDistFromP1);
|
|
|
|
const cvf::Vec3d v = p2 - p1;
|
|
|
|
(*normalizedDistFromP1) = 0.0;
|
|
|
|
double denominator = -(plane.A()*v.x() + plane.B()*v.y() + plane.C()*v.z());
|
|
if (denominator != 0)
|
|
{
|
|
double u = (plane.A()*p1.x() + plane.B()*p1.y() + plane.C()*p1.z() + plane.D()) / denominator;
|
|
(*normalizedDistFromP1) = u;
|
|
if (u > 0.0 && u < 1.0)
|
|
{
|
|
return (p1 + u*v);
|
|
}
|
|
else
|
|
{
|
|
if (u >= 1.0)
|
|
{
|
|
return p2;
|
|
}
|
|
else
|
|
{
|
|
return p1;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
return p1;
|
|
}
|
|
}
|
|
|
|
//--------------------------------------------------------------------------------------------------
|
|
/// Based on description and implementation from Paul Bourke:
|
|
///
|
|
/// http://paulbourke.net/geometry/polygonise/
|
|
///
|
|
/// Note that the element is turned inside-out compared to what we use elsewhere in caf/ResInsight
|
|
/// So the winding of all the sides are opposite.
|
|
/// 4-----4------5
|
|
/// /| /| k POS_I = 0
|
|
/// 7 8 5 9 | NEG_I = 1
|
|
/// / | / | | POS_J = 2
|
|
/// 7------6-----6 | | NEG_J = 3
|
|
/// | 0-----0--|---1 *------i POS_K = 4
|
|
/// 11 / 10 / / NEG_K = 5
|
|
/// | 3 | 1 / NO_FACE = 6
|
|
/// |/ |/ j
|
|
/// 3------2-----2
|
|
///
|
|
// The cellFaceForEachTriangleEdge refer to the edge after the corresponding triangle vertex.
|
|
//--------------------------------------------------------------------------------------------------
|
|
int HexGridIntersectionTools::planeHexIntersectionMC(const cvf::Plane& plane,
|
|
const cvf::Vec3d cell[8],
|
|
const size_t hexCornersIds[8],
|
|
std::vector<ClipVx>* triangleVxes,
|
|
std::vector<int>* cellFaceForEachTriangleEdge)
|
|
{
|
|
|
|
|
|
|
|
static const cvf::uint cubeIdxToCutEdgeBitfield[256] =
|
|
{
|
|
0x0, 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
|
|
0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
|
|
0x190, 0x99, 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
|
|
0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
|
|
0x230, 0x339, 0x33, 0x13a, 0x636, 0x73f, 0x435, 0x53c,
|
|
0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
|
|
0x3a0, 0x2a9, 0x1a3, 0xaa, 0x7a6, 0x6af, 0x5a5, 0x4ac,
|
|
0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
|
|
0x460, 0x569, 0x663, 0x76a, 0x66, 0x16f, 0x265, 0x36c,
|
|
0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
|
|
0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff, 0x3f5, 0x2fc,
|
|
0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
|
|
0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55, 0x15c,
|
|
0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
|
|
0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc,
|
|
0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
|
|
0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
|
|
0xcc, 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
|
|
0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
|
|
0x15c, 0x55, 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
|
|
0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
|
|
0x2fc, 0x3f5, 0xff, 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
|
|
0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
|
|
0x36c, 0x265, 0x16f, 0x66, 0x76a, 0x663, 0x569, 0x460,
|
|
0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
|
|
0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa, 0x1a3, 0x2a9, 0x3a0,
|
|
0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
|
|
0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33, 0x339, 0x230,
|
|
0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
|
|
0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99, 0x190,
|
|
0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
|
|
0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0
|
|
};
|
|
|
|
static const int cubeIdxToTriangleIndices[256][16] =
|
|
{
|
|
{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1 },
|
|
{ 8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1 },
|
|
{ 3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1 },
|
|
{ 4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1 },
|
|
{ 4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1 },
|
|
{ 9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1 },
|
|
{ 10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1 },
|
|
{ 5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1 },
|
|
{ 5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1 },
|
|
{ 8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1 },
|
|
{ 2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1 },
|
|
{ 2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1 },
|
|
{ 11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1 },
|
|
{ 5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1 },
|
|
{ 11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1 },
|
|
{ 11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1 },
|
|
{ 2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1 },
|
|
{ 6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1 },
|
|
{ 3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1 },
|
|
{ 6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1 },
|
|
{ 6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1 },
|
|
{ 8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1 },
|
|
{ 7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1 },
|
|
{ 3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1 },
|
|
{ 0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1 },
|
|
{ 9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1 },
|
|
{ 8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1 },
|
|
{ 5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1 },
|
|
{ 0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1 },
|
|
{ 6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1 },
|
|
{ 10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1 },
|
|
{ 1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1 },
|
|
{ 0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1 },
|
|
{ 3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1 },
|
|
{ 6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1 },
|
|
{ 9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1 },
|
|
{ 8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1 },
|
|
{ 3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1 },
|
|
{ 10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1 },
|
|
{ 10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1 },
|
|
{ 2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1 },
|
|
{ 7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1 },
|
|
{ 2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1 },
|
|
{ 1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1 },
|
|
{ 11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1 },
|
|
{ 8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1 },
|
|
{ 0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1 },
|
|
{ 7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1 },
|
|
{ 7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1 },
|
|
{ 10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1 },
|
|
{ 0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1 },
|
|
{ 7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1 },
|
|
{ 6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1 },
|
|
{ 4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1 },
|
|
{ 10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1 },
|
|
{ 8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1 },
|
|
{ 1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1 },
|
|
{ 10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1 },
|
|
{ 10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1 },
|
|
{ 9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1 },
|
|
{ 7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1 },
|
|
{ 3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1 },
|
|
{ 7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1 },
|
|
{ 3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1 },
|
|
{ 6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1 },
|
|
{ 9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1 },
|
|
{ 1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1 },
|
|
{ 4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1 },
|
|
{ 7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1 },
|
|
{ 6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1 },
|
|
{ 0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1 },
|
|
{ 6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1 },
|
|
{ 0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1 },
|
|
{ 11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1 },
|
|
{ 6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1 },
|
|
{ 5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1 },
|
|
{ 9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1 },
|
|
{ 1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1 },
|
|
{ 10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1 },
|
|
{ 0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1 },
|
|
{ 11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1 },
|
|
{ 9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1 },
|
|
{ 7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1 },
|
|
{ 2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1 },
|
|
{ 9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1 },
|
|
{ 9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1 },
|
|
{ 1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1 },
|
|
{ 0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1 },
|
|
{ 10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1 },
|
|
{ 2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1 },
|
|
{ 0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1 },
|
|
{ 0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1 },
|
|
{ 9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1 },
|
|
{ 5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1 },
|
|
{ 5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1 },
|
|
{ 8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1 },
|
|
{ 9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1 },
|
|
{ 1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1 },
|
|
{ 3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1 },
|
|
{ 4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1 },
|
|
{ 9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1 },
|
|
{ 11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1 },
|
|
{ 2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1 },
|
|
{ 9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1 },
|
|
{ 3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1 },
|
|
{ 1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1 },
|
|
{ 4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1 },
|
|
{ 0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1 },
|
|
{ 1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ 0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
|
|
{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }
|
|
};
|
|
|
|
static const int edgeTable[12][2] =
|
|
{
|
|
{0, 1},
|
|
{1, 2},
|
|
{2, 3},
|
|
{3, 0},
|
|
{4, 5},
|
|
{5, 6},
|
|
{6, 7},
|
|
{7, 4},
|
|
{0, 4},
|
|
{1, 5},
|
|
{2, 6},
|
|
{3, 7}
|
|
};
|
|
|
|
int cubeIndex = 0;
|
|
if (plane.distanceSquared(cell[0]) < 0) cubeIndex |= 1;
|
|
if (plane.distanceSquared(cell[1]) < 0) cubeIndex |= 2;
|
|
if (plane.distanceSquared(cell[2]) < 0) cubeIndex |= 4;
|
|
if (plane.distanceSquared(cell[3]) < 0) cubeIndex |= 8;
|
|
if (plane.distanceSquared(cell[4]) < 0) cubeIndex |= 16;
|
|
if (plane.distanceSquared(cell[5]) < 0) cubeIndex |= 32;
|
|
if (plane.distanceSquared(cell[6]) < 0) cubeIndex |= 64;
|
|
if (plane.distanceSquared(cell[7]) < 0) cubeIndex |= 128;
|
|
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] == 0)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
cvf::Vec3d edgeIntersections[12];
|
|
double normDistAlongEdge[12];
|
|
|
|
|
|
// Compute vertex coordinates on the edges where we have intersections
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 1) edgeIntersections[0] = planeLineIntersectionForMC(plane, cell[0], cell[1], &normDistAlongEdge[0]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 2) edgeIntersections[1] = planeLineIntersectionForMC(plane, cell[1], cell[2], &normDistAlongEdge[1]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 4) edgeIntersections[2] = planeLineIntersectionForMC(plane, cell[2], cell[3], &normDistAlongEdge[2]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 8) edgeIntersections[3] = planeLineIntersectionForMC(plane, cell[3], cell[0], &normDistAlongEdge[3]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 16) edgeIntersections[4] = planeLineIntersectionForMC(plane, cell[4], cell[5], &normDistAlongEdge[4]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 32) edgeIntersections[5] = planeLineIntersectionForMC(plane, cell[5], cell[6], &normDistAlongEdge[5]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 64) edgeIntersections[6] = planeLineIntersectionForMC(plane, cell[6], cell[7], &normDistAlongEdge[6]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 128) edgeIntersections[7] = planeLineIntersectionForMC(plane, cell[7], cell[4], &normDistAlongEdge[7]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 256) edgeIntersections[8] = planeLineIntersectionForMC(plane, cell[0], cell[4], &normDistAlongEdge[8]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 512) edgeIntersections[9] = planeLineIntersectionForMC(plane, cell[1], cell[5], &normDistAlongEdge[9]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 1024) edgeIntersections[10] = planeLineIntersectionForMC(plane, cell[2], cell[6], &normDistAlongEdge[10]);
|
|
if (cubeIdxToCutEdgeBitfield[cubeIndex] & 2048) edgeIntersections[11] = planeLineIntersectionForMC(plane, cell[3], cell[7], &normDistAlongEdge[11]);
|
|
|
|
|
|
// Create the triangles
|
|
|
|
const int* triangleIndicesToCubeEdges = cubeIdxToTriangleIndices[cubeIndex];
|
|
cvf::uint triangleVxIdx = 0;
|
|
|
|
int cubeEdgeIdx = triangleIndicesToCubeEdges[triangleVxIdx];
|
|
while (cubeEdgeIdx != -1)
|
|
{
|
|
ClipVx cvx;
|
|
cvx.vx = edgeIntersections[cubeEdgeIdx];
|
|
cvx.normDistFromEdgeVx1 = normDistAlongEdge[cubeEdgeIdx];
|
|
cvx.clippedEdgeVx1Id = hexCornersIds[edgeTable[cubeEdgeIdx][0]];
|
|
cvx.clippedEdgeVx2Id = hexCornersIds[edgeTable[cubeEdgeIdx][1]];
|
|
|
|
(*triangleVxes).push_back(cvx);
|
|
++triangleVxIdx;
|
|
|
|
cubeEdgeIdx = triangleIndicesToCubeEdges[triangleVxIdx];
|
|
}
|
|
|
|
cvf::uint triangleCount = triangleVxIdx / 3;
|
|
|
|
static const int edgeEdgeCutsToCellFace[12][12] = {
|
|
// 0 1 2 3 4 5 6 7 8 9 10 11
|
|
{ 6, 5, 5, 5, 3, 6, 6, 6, 3, 3, 6, 6 }, // 0
|
|
{ 5, 6, 5, 5, 6, 0, 6, 6, 6, 0, 0, 6 }, // 1 POS_I = 0
|
|
{ 5, 5, 6, 5, 6, 6, 2, 6, 6, 6, 2, 2 }, // 2 NEG_I = 1
|
|
{ 5, 5, 5, 6, 6, 6, 6, 1, 1, 6, 6, 1 }, // 3 POS_J = 2
|
|
{ 3, 6, 6, 6, 6, 4, 4, 4, 3, 3, 6, 6 }, // 4 NEG_J = 3
|
|
{ 6, 0, 6, 6, 4, 6, 4, 4, 6, 0, 0, 6 }, // 5 POS_K = 4
|
|
{ 6, 6, 2, 6, 4, 4, 6, 4, 6, 6, 2, 2 }, // 6 NEG_K = 5
|
|
{ 6, 6, 6, 1, 4, 4, 4, 6, 1, 6, 6, 1 }, // 7 NO_FACE = 6
|
|
{ 3, 6, 6, 1, 3, 6, 6, 1, 6, 3, 6, 1 }, // 8
|
|
{ 3, 0, 6, 6, 3, 0, 6, 6, 3, 6, 0, 6 }, // 9
|
|
{ 6, 0, 2, 6, 6, 0, 2, 6, 6, 0, 6, 2 }, // 10
|
|
{ 6, 6, 2, 1, 6, 6, 2, 1, 1, 6, 2, 6 } // 11
|
|
};
|
|
|
|
|
|
(*cellFaceForEachTriangleEdge).clear();
|
|
(*cellFaceForEachTriangleEdge).resize(triangleVxIdx, 6);
|
|
|
|
for (cvf::uint tIdx = 0; tIdx < triangleCount; ++tIdx)
|
|
{
|
|
cvf::uint triVxIdx = 3 * tIdx;
|
|
|
|
int cubeEdgeIdx1 = triangleIndicesToCubeEdges[triVxIdx];
|
|
int cubeEdgeIdx2 = triangleIndicesToCubeEdges[triVxIdx + 1];
|
|
int cubeEdgeIdx3 = triangleIndicesToCubeEdges[triVxIdx + 2];
|
|
|
|
(*cellFaceForEachTriangleEdge)[triVxIdx + 0] = edgeEdgeCutsToCellFace[cubeEdgeIdx1][cubeEdgeIdx2];
|
|
(*cellFaceForEachTriangleEdge)[triVxIdx + 1] = edgeEdgeCutsToCellFace[cubeEdgeIdx2][cubeEdgeIdx3];
|
|
(*cellFaceForEachTriangleEdge)[triVxIdx + 2] = edgeEdgeCutsToCellFace[cubeEdgeIdx3][cubeEdgeIdx1];
|
|
}
|
|
|
|
|
|
#if 0
|
|
// Calculate what triangle edges are representing the cut of a cell face
|
|
// Do this by counting the times two specific cube edges are used for a triangle edge.
|
|
// Internal edges will have a count of 2, while external edges only 1
|
|
|
|
(*isTriEdgeCellContour).clear();
|
|
(*isTriEdgeCellContour).resize(triangleVxIdx);
|
|
|
|
|
|
int triangleEdgeCount[12][12] = {
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
|
|
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }
|
|
};
|
|
|
|
(*isTriEdgeCellContour).clear();
|
|
(*isTriEdgeCellContour).resize(triangleVxIdx, false);
|
|
|
|
for (cvf::uint tIdx = 0; tIdx < triangleCount; ++tIdx)
|
|
{
|
|
cvf::uint triVxIdx = 3 * tIdx;
|
|
int cubeEdgeIdx1 = triangleIndicesToCubeEdges[triVxIdx];
|
|
int cubeEdgeIdx2 = triangleIndicesToCubeEdges[triVxIdx + 1];
|
|
int cubeEdgeIdx3 = triangleIndicesToCubeEdges[triVxIdx + 2];
|
|
|
|
cubeEdgeIdx1 < cubeEdgeIdx2 ? ++triangleEdgeCount[cubeEdgeIdx1][cubeEdgeIdx2] : ++triangleEdgeCount[cubeEdgeIdx2][cubeEdgeIdx1];
|
|
cubeEdgeIdx2 < cubeEdgeIdx3 ? ++triangleEdgeCount[cubeEdgeIdx2][cubeEdgeIdx3] : ++triangleEdgeCount[cubeEdgeIdx3][cubeEdgeIdx2];
|
|
cubeEdgeIdx3 < cubeEdgeIdx1 ? ++triangleEdgeCount[cubeEdgeIdx3][cubeEdgeIdx1] : ++triangleEdgeCount[cubeEdgeIdx1][cubeEdgeIdx3];
|
|
}
|
|
|
|
for (cvf::uint tIdx = 0; tIdx < triangleCount; ++tIdx)
|
|
{
|
|
cvf::uint triVxIdx = 3 * tIdx;
|
|
|
|
int cubeEdgeIdx1 = triangleIndicesToCubeEdges[triVxIdx];
|
|
int cubeEdgeIdx2 = triangleIndicesToCubeEdges[triVxIdx + 1];
|
|
int cubeEdgeIdx3 = triangleIndicesToCubeEdges[triVxIdx + 2];
|
|
|
|
// We have a contour if the count is exactly 1.
|
|
|
|
(*isTriEdgeCellContour)[triVxIdx + 0] = (1 == (cubeEdgeIdx1 < cubeEdgeIdx2 ? triangleEdgeCount[cubeEdgeIdx1][cubeEdgeIdx2] : triangleEdgeCount[cubeEdgeIdx2][cubeEdgeIdx1]));
|
|
(*isTriEdgeCellContour)[triVxIdx + 1] = (1 == (cubeEdgeIdx2 < cubeEdgeIdx3 ? triangleEdgeCount[cubeEdgeIdx2][cubeEdgeIdx3] : triangleEdgeCount[cubeEdgeIdx3][cubeEdgeIdx2]));
|
|
(*isTriEdgeCellContour)[triVxIdx + 2] = (1 == (cubeEdgeIdx3 < cubeEdgeIdx1 ? triangleEdgeCount[cubeEdgeIdx3][cubeEdgeIdx1] : triangleEdgeCount[cubeEdgeIdx1][cubeEdgeIdx3]));
|
|
}
|
|
|
|
#endif
|
|
return triangleCount;
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
//--------------------------------------------------------------------------------------------------
|
|
/// Based on description and implementation from Paul Bourke:
|
|
///
|
|
/// http://paulbourke.net/geometry/polygonise/
|
|
///
|
|
/// Note that the element is turned inside-out compared to what we use elsewhere in caf/ResInsight
|
|
/// So the winding of all the sides are opposite.
|
|
/// 4-----4------5
|
|
/// /| /| k POS_I = 0
|
|
/// 7 8 5 9 | NEG_I = 1
|
|
/// / | / | | POS_J = 2
|
|
/// 7------6-----6 | | NEG_J = 3
|
|
/// | 0-----0--|---1 *------i POS_K = 4
|
|
/// 11 / 10 / / NEG_K = 5
|
|
/// | 3 | 1 / NO_FACE = 6
|
|
/// |/ |/ j
|
|
/// 3------2-----2
|
|
///
|
|
// The cellFaceForEachTriangleEdge refer to the edge after the corresponding triangle vertex.
|
|
|
|
/*
|
|
Based on description and implementation from Paul Bourke:
|
|
http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/
|
|
|
|
Polygonise a tetrahedron given its vertices within a cube
|
|
This is an alternative algorithm to polygonisegrid.
|
|
It results in a smoother surface but more triangular facets.
|
|
|
|
+ 0 + 0
|
|
/|\ /|\
|
|
/ | \ / | \
|
|
/ | \ / | \
|
|
/ | \ / | \
|
|
/ | \ / 2 | \
|
|
/ | \ / __--+_ \
|
|
+-------------+ 1 3 +--__ --_ \
|
|
3 \ | / ---__ --_\
|
|
\ | / ---__-\
|
|
\ | / --+ 1
|
|
\ | /
|
|
\ | /
|
|
\|/ 2 is behind 1 and 3
|
|
+ 2
|
|
|
|
|
|
Build six tets from a cube to make sure the split direction is equal for opposite sides.
|
|
Surface normals are pointing outward.
|
|
|
|
See following comment is taken from http://www.iue.tuwien.ac.at/phd/wessner/node32.html
|
|
The decompositions of a cube into five tetrahedra yields an orientation switch of two opposite diagonal face edges of the cube.
|
|
Due to this fact, the tessellation of one cube, as part of a larger cubic grid, forces a particular tessellation of all neighboring cubes to guarantee a conformal mesh.
|
|
This means that, if such five-decompositions cubes are stacked together to a chain, the mesh of each cube must be rotated by an angle of 90 deg
|
|
|
|
The tessellation makes sure opposite faces are divided along the same line
|
|
See figure http://www.ics.uci.edu/~eppstein/projects/tetra/
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|
|
|
4, 5, 6, 0
|
|
0, 1, 5, 6
|
|
0, 2, 1, 6
|
|
4, 6, 7, 0
|
|
0, 7, 3, 6
|
|
0, 3, 2, 6
|
|
|
|
Introduces the additional diagonal edges in the Hex from 12 up to and including 18:
|
|
0 2 // 12 NEG_K
|
|
0 5 // 13 NEG_J
|
|
1 6 // 14 POS_I
|
|
3 6 // 15 POS_J
|
|
0 7 // 16 NEG_I
|
|
4 6 // 17 POS_K
|
|
0 6 // 18 Internal Diagonal
|
|
|
|
/// 4-----4------5
|
|
/// /| /| k POS_I = 0
|
|
/// 7 8 17 5 9 | NEG_I = 1
|
|
/// / | 13 / | | POS_J = 2
|
|
/// 7------6-----6 14| | NEG_J = 3
|
|
/// |16 0-----0--|---1 *------i POS_K = 4
|
|
/// 11 / 15 10 / / NEG_K = 5
|
|
/// | 3 12 | 1 / NO_FACE = 6
|
|
/// |/ |/ j
|
|
/// 3------2-----2
|
|
|
|
|
|
*/
|
|
//--------------------------------------------------------------------------------------------------
|
|
int HexGridIntersectionTools::planeHexIntersectionMCTet( const cvf::Plane& plane,
|
|
const cvf::Vec3d cell[8],
|
|
const size_t hexCornersIds[8],
|
|
std::vector<ClipVx>* triangleVxes,
|
|
std::vector<int>* cellFaceForEachTriangleEdge )
|
|
{
|
|
std::array<double, 8> cellCornerSqDistToPlane =
|
|
{
|
|
plane.distanceSquared( cell[0] ),
|
|
plane.distanceSquared( cell[1] ),
|
|
plane.distanceSquared( cell[2] ),
|
|
plane.distanceSquared( cell[3] ),
|
|
plane.distanceSquared( cell[4] ),
|
|
plane.distanceSquared( cell[5] ),
|
|
plane.distanceSquared( cell[6] ),
|
|
plane.distanceSquared( cell[7] ),
|
|
};
|
|
|
|
int cubeIndex = 0;
|
|
if (cellCornerSqDistToPlane[0] < 0) cubeIndex |= 1;
|
|
if (cellCornerSqDistToPlane[1] < 0) cubeIndex |= 2;
|
|
if (cellCornerSqDistToPlane[2] < 0) cubeIndex |= 4;
|
|
if (cellCornerSqDistToPlane[3] < 0) cubeIndex |= 8;
|
|
if (cellCornerSqDistToPlane[4] < 0) cubeIndex |= 16;
|
|
if (cellCornerSqDistToPlane[5] < 0) cubeIndex |= 32;
|
|
if (cellCornerSqDistToPlane[6] < 0) cubeIndex |= 64;
|
|
if (cellCornerSqDistToPlane[7] < 0) cubeIndex |= 128;
|
|
|
|
if (cubeIndex == 0 || cubeIndex == 255) return 0;
|
|
|
|
|
|
int tetCount = 0;
|
|
tetCount += planeMcTetIntersection(plane, cell, hexCornersIds, cellCornerSqDistToPlane.data(), { 4, 5, 6, 0 }, triangleVxes, cellFaceForEachTriangleEdge );
|
|
tetCount += planeMcTetIntersection(plane, cell, hexCornersIds, cellCornerSqDistToPlane.data(), { 0, 1, 5, 6 }, triangleVxes, cellFaceForEachTriangleEdge );
|
|
tetCount += planeMcTetIntersection(plane, cell, hexCornersIds, cellCornerSqDistToPlane.data(), { 0, 2, 1, 6 }, triangleVxes, cellFaceForEachTriangleEdge );
|
|
tetCount += planeMcTetIntersection(plane, cell, hexCornersIds, cellCornerSqDistToPlane.data(), { 4, 6, 7, 0 }, triangleVxes, cellFaceForEachTriangleEdge );
|
|
tetCount += planeMcTetIntersection(plane, cell, hexCornersIds, cellCornerSqDistToPlane.data(), { 0, 7, 3, 6 }, triangleVxes, cellFaceForEachTriangleEdge );
|
|
tetCount += planeMcTetIntersection(plane, cell, hexCornersIds, cellCornerSqDistToPlane.data(), { 0, 3, 2, 6 }, triangleVxes, cellFaceForEachTriangleEdge );
|
|
|
|
return tetCount;
|
|
}
|
|
|
|
|
|
|
|
//--------------------------------------------------------------------------------------------------
|
|
///
|
|
//--------------------------------------------------------------------------------------------------
|
|
cvf::uint HexGridIntersectionTools::planeMcTetIntersection( const cvf::Plane& plane,
|
|
const cvf::Vec3d hexCell[8],
|
|
const size_t hexCornersIds[8],
|
|
const double cornerDistToPlane[8],
|
|
const std::array<int, 4> & tetCell,
|
|
std::vector<ClipVx>* triangleVxes,
|
|
std::vector<int>* cellFaceForEachTriangleEdge )
|
|
{
|
|
static const int edgeEdgeCutsToCellFace[19][19] = {
|
|
// 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 4--------------4---------------5
|
|
{ 6, 5, 5, 5, 3, 6, 6, 6, 3, 3, 6, 6, 5, 3, 6, 6, 6, 6, 6 }, // 0 /|\__ __//|
|
|
{ 5, 6, 5, 5, 6, 0, 6, 6, 6, 0, 0, 6, 5, 6, 0, 6, 6, 6, 6 }, // 1 POS_I = 0 / | \___ _/ / |
|
|
{ 5, 5, 6, 5, 6, 6, 2, 6, 6, 6, 2, 2, 5, 6, 6, 2, 6, 6, 6 }, // 2 NEG_I = 1 7 | \__ __/ / | k
|
|
{ 5, 5, 5, 6, 6, 6, 6, 1, 1, 6, 6, 1, 5, 6, 6, 6, 1, 6, 6 }, // 3 POS_J = 2 / | 17___ _/ 5 | |
|
|
{ 3, 6, 6, 6, 6, 4, 4, 4, 3, 3, 6, 6, 6, 3, 6, 6, 6, 4, 6 }, // 4 NEG_J = 3 / 8 \___ / 9 |
|
|
{ 6, 0, 6, 6, 4, 6, 4, 4, 6, 0, 0, 6, 6, 6, 0, 6, 6, 4, 6 }, // 5 POS_K = 4 / | __/ \___ / | |
|
|
{ 6, 6, 2, 6, 4, 4, 6, 4, 6, 6, 2, 2, 6, 6, 6, 2, 6, 4, 6 }, // 6 NEG_K = 5 7---------------6--------------6 | *------i
|
|
{ 6, 6, 6, 1, 4, 4, 4, 6, 1, 6, 6, 1, 6, 6, 6, 6, 1, 4, 6 }, // 7 NO_FACE = 6 |\_ | __13 ____/_/|\_ | /
|
|
{ 3, 6, 6, 1, 3, 6, 6, 1, 6, 3, 6, 1, 6, 3, 6, 6, 1, 6, 6 }, // 8 | 16 | __/ _18_/ __/ | 14 | /
|
|
{ 3, 0, 6, 6, 3, 0, 6, 6, 3, 6, 0, 6, 6, 3, 0, 6, 6, 6, 6 }, // 9 | \_ | __/____/ _/ | \_ | j
|
|
{ 6, 0, 2, 6, 6, 0, 2, 6, 6, 0, 6, 2, 6, 6, 0, 2, 6, 6, 6 }, // 10 | \|__/__/ __/ | \|
|
|
{ 6, 6, 2, 1, 6, 6, 2, 1, 1, 6, 2, 6, 6, 6, 6, 2, 1, 6, 6 }, // 11 | 0-----------_/----0-----|------1
|
|
{ 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 }, // 12 11 / \__ __15 10 /
|
|
{ 3, 6, 6, 6, 3, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6 }, // 13 | / \_ _/ | /
|
|
{ 6, 0, 6, 6, 6, 0, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6 }, // 14 | 3 __/ \___ | 1
|
|
{ 6, 6, 2, 6, 6, 6, 2, 6, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 6 }, // 15 | / __/ 12__ | /
|
|
{ 6, 6, 6, 1, 6, 6, 6, 1, 1, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6 }, // 16 | / __/ \___ | /
|
|
{ 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 }, // 17 |/__/ \___|/
|
|
{ 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 }, // 18 3---------------2--------------2
|
|
};
|
|
|
|
static const int cellCornerCellCornerToEdge[8][8] = {
|
|
// 0 1 2 3 4 5 6 7
|
|
{ -1, 0, 12, 3, 8, 13, 18, 16 }, // 0
|
|
{ 0, -1, 1, -1, -1, 9, 14, -1 }, // 1
|
|
{ 12, 1, -1, 2, -1, -1, 10, -1 }, // 2
|
|
{ 3, -1, 2, -1, -1, -1, 15, 11 }, // 3
|
|
{ 8, -1, -1, -1, -1, 4, 17, 7 }, // 4
|
|
{ 13, 9, -1, -1, 4, -1, 5, -1 }, // 5
|
|
{ 18, 14, 10, 15, 17, 5, -1, 6 }, // 6
|
|
{ 16, -1, -1, 11, 7, -1, 6, -1 }, // 7
|
|
};
|
|
|
|
|
|
cvf::uint ntri = 0;
|
|
|
|
int triindex = 0;
|
|
if( cornerDistToPlane[tetCell[0]] < 0 ) triindex |= 1;
|
|
if( cornerDistToPlane[tetCell[1]] < 0 ) triindex |= 2;
|
|
if( cornerDistToPlane[tetCell[2]] < 0 ) triindex |= 4;
|
|
if( cornerDistToPlane[tetCell[3]] < 0 ) triindex |= 8;
|
|
|
|
auto clipEdgeFunc = [&]( int hexCornerIdx0, int hexCornerIdx1 )
|
|
{
|
|
ClipVx cvx;
|
|
cvx.vx = planeLineIntersectionForMC( plane, hexCell[hexCornerIdx0], hexCell[hexCornerIdx1], &cvx.normDistFromEdgeVx1 );
|
|
cvx.clippedEdgeVx1Id = hexCornersIds[hexCornerIdx0];
|
|
cvx.clippedEdgeVx2Id = hexCornersIds[hexCornerIdx1];
|
|
return cvx;
|
|
};
|
|
|
|
auto addCellFaceStatusForTriangleEdges = [&]( int e11, int e12,
|
|
int e21, int e22,
|
|
int e31, int e32)
|
|
{
|
|
int cutEdge1 = cellCornerCellCornerToEdge[e11][e12];
|
|
int cutEdge2 = cellCornerCellCornerToEdge[e21][e22];
|
|
int cutEdge3 = cellCornerCellCornerToEdge[e31][e32];
|
|
|
|
CVF_ASSERT(cutEdge1 >= 0);
|
|
CVF_ASSERT(cutEdge2 >= 0);
|
|
CVF_ASSERT(cutEdge3 >= 0);
|
|
|
|
cellFaceForEachTriangleEdge->emplace_back( edgeEdgeCutsToCellFace[cutEdge1][cutEdge2] );
|
|
cellFaceForEachTriangleEdge->emplace_back( edgeEdgeCutsToCellFace[cutEdge2][cutEdge3] );
|
|
cellFaceForEachTriangleEdge->emplace_back( edgeEdgeCutsToCellFace[cutEdge3][cutEdge1] );
|
|
};
|
|
|
|
switch( triindex ) {
|
|
case 0x00:
|
|
case 0x0F:
|
|
break;
|
|
case 0x0E:
|
|
case 0x01:
|
|
{
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[0], tetCell[1] ) );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[0], tetCell[2] ) );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[0], tetCell[3] ) );
|
|
|
|
addCellFaceStatusForTriangleEdges(tetCell[0], tetCell[1],
|
|
tetCell[0], tetCell[2],
|
|
tetCell[0], tetCell[3]);
|
|
ntri++;
|
|
}
|
|
break;
|
|
case 0x0D:
|
|
case 0x02:
|
|
{
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[1], tetCell[0] ) );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[1], tetCell[3] ) );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[1], tetCell[2] ) );
|
|
|
|
addCellFaceStatusForTriangleEdges( tetCell[1], tetCell[0],
|
|
tetCell[1], tetCell[3],
|
|
tetCell[1], tetCell[2] );
|
|
ntri++;
|
|
}
|
|
break;
|
|
case 0x0C:
|
|
case 0x03:
|
|
{
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[0], tetCell[3] ) );
|
|
ClipVx vx1 = clipEdgeFunc( tetCell[0], tetCell[2] );
|
|
triangleVxes->push_back( vx1 );
|
|
ClipVx vx2 = clipEdgeFunc( tetCell[1], tetCell[3] );
|
|
triangleVxes->push_back( vx2 );
|
|
|
|
|
|
addCellFaceStatusForTriangleEdges( tetCell[0], tetCell[3],
|
|
tetCell[0], tetCell[2],
|
|
tetCell[1], tetCell[3] );
|
|
|
|
ntri++;
|
|
|
|
|
|
triangleVxes->push_back( vx2 );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[1], tetCell[2] ) );
|
|
triangleVxes->push_back( vx1 );
|
|
|
|
addCellFaceStatusForTriangleEdges( tetCell[1], tetCell[3],
|
|
tetCell[1], tetCell[2],
|
|
tetCell[0], tetCell[2] );
|
|
ntri++;
|
|
}
|
|
break;
|
|
case 0x0B:
|
|
case 0x04:
|
|
{
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[2], tetCell[0] ) );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[2], tetCell[1] ) );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[2], tetCell[3] ) );
|
|
|
|
addCellFaceStatusForTriangleEdges( tetCell[2], tetCell[0],
|
|
tetCell[2], tetCell[1],
|
|
tetCell[2], tetCell[3] );
|
|
ntri++;
|
|
}
|
|
break;
|
|
case 0x0A:
|
|
case 0x05:
|
|
{
|
|
ClipVx vx0 = clipEdgeFunc( tetCell[0], tetCell[1] );
|
|
triangleVxes->push_back( vx0 );
|
|
ClipVx vx1 = clipEdgeFunc( tetCell[2], tetCell[3] );
|
|
triangleVxes->push_back( vx1 );
|
|
ClipVx vx2 = clipEdgeFunc( tetCell[0], tetCell[3] );
|
|
triangleVxes->push_back( vx2 );
|
|
|
|
addCellFaceStatusForTriangleEdges( tetCell[0], tetCell[1],
|
|
tetCell[2], tetCell[3],
|
|
tetCell[0], tetCell[3] );
|
|
ntri++;
|
|
|
|
triangleVxes->push_back( vx0 );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[1], tetCell[2] ) );
|
|
triangleVxes->push_back( vx1 );
|
|
|
|
addCellFaceStatusForTriangleEdges( tetCell[0], tetCell[1],
|
|
tetCell[1], tetCell[2],
|
|
tetCell[2], tetCell[3] );
|
|
|
|
ntri++;
|
|
}
|
|
break;
|
|
case 0x09:
|
|
case 0x06:
|
|
{
|
|
ClipVx vx0 = clipEdgeFunc( tetCell[0], tetCell[1] );
|
|
triangleVxes->push_back( vx0 );
|
|
ClipVx vx1 = clipEdgeFunc( tetCell[1], tetCell[3] );
|
|
triangleVxes->push_back( vx1 );
|
|
ClipVx vx2 = clipEdgeFunc( tetCell[2], tetCell[3] );
|
|
triangleVxes->push_back( vx2 );
|
|
|
|
addCellFaceStatusForTriangleEdges( tetCell[0], tetCell[1],
|
|
tetCell[1], tetCell[3],
|
|
tetCell[2], tetCell[3] );
|
|
|
|
ntri++;
|
|
|
|
triangleVxes->push_back( vx0 );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[0], tetCell[2] ) );
|
|
triangleVxes->push_back( vx2 );
|
|
|
|
addCellFaceStatusForTriangleEdges( tetCell[0], tetCell[1],
|
|
tetCell[0], tetCell[2],
|
|
tetCell[2], tetCell[3] );
|
|
|
|
ntri++;
|
|
}
|
|
break;
|
|
case 0x07:
|
|
case 0x08:
|
|
{
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[3], tetCell[0] ) );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[3], tetCell[2] ) );
|
|
triangleVxes->emplace_back( clipEdgeFunc( tetCell[3], tetCell[1] ) );
|
|
|
|
addCellFaceStatusForTriangleEdges( tetCell[3], tetCell[0],
|
|
tetCell[3], tetCell[2],
|
|
tetCell[3], tetCell[1] );
|
|
|
|
ntri++;
|
|
}
|
|
break;
|
|
}
|
|
|
|
return ntri;
|
|
|
|
}
|
|
|
|
} // namespace cvf
|
|
|