#2608 Fix error in analythical control point based S-Curve calculation.

Seed SolveSpace solution with estimated solution.
Add (disabled) test covering all configurations of curves for ctl point based curve
This commit is contained in:
Jacob Støren 2018-08-09 12:54:54 +02:00
parent 1fff2dfa97
commit 5cdde7f851
3 changed files with 322 additions and 83 deletions

View File

@ -2,6 +2,8 @@
#include "SolveSpaceSystem.h"
#include <cmath>
#include "cvfMatrix4.h"
#include <iostream>
//--------------------------------------------------------------------------------------------------
///
@ -9,6 +11,8 @@
RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1, double rad1,
cvf::Vec3d p2, double azi2, double inc2, double rad2)
: m_isCalculationOK(false)
, m_p1(p1)
, m_p2(p2)
, m_firstArcEndpoint(p1 + 0.3*(p2-p1))
, m_secondArcStartpoint(p1 + 0.6*(p2-p1))
, m_r1(rad1)
@ -48,28 +52,24 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
&est_p_Plane2Qx,
&est_p_Plane2Qy,
&est_p_Plane2Qz);
double est_rad1 = rad1;
double est_rad2 = rad2;
if (false)
if (true)
{
double p1p2Length = (p2-p1).length();
RiaSCurveCalculator estimatedCurveCalc = RiaSCurveCalculator::fromTangentsAndLength(p1, azi1, inc1, 0.2 * p1p2Length,
p2, azi2, inc2, 0.2 * p1p2Length);
est_p_c1x = 0.0;
est_p_c1y = rad1;
est_p_p11x = rad1;
est_p_p11y = rad1;
//est_rad1 = estimatedCurveCalc.firstRadius();
//est_rad2 = estimatedCurveCalc.secondRadius();
est_p_c2x = 0.0;
est_p_c2y = rad2;
est_p_p22x = -rad2;
est_p_p22y = rad2;
#if 0
cvf::Vec3d est_tp1c1;
cvf::Vec3d est_tp2c2;
est_tp1c1 = (estimatedCurveCalc.firstCenter() - p1).getNormalized();
est_tp2c2 = (estimatedCurveCalc.secondCenter() - p2).getNormalized();
std::cout << "Estimate:" << std::endl;
estimatedCurveCalc.dump();
#endif
cvf::Vec3d t1(sin(azi1)*sin(inc1),
cos(azi1)*sin(inc1),
@ -78,6 +78,30 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
cos(azi2)*sin(inc2),
-cos(inc2));
cvf::Vec3d est_tp1c1 = (estimatedCurveCalc.firstCenter() - p1).getNormalized();
cvf::Vec3d est_tp2c2 = (estimatedCurveCalc.secondCenter() - p2).getNormalized();
cvf::Mat4d mx1 = cvf::Mat4d::fromCoordSystemAxes(&t1, &est_tp1c1, nullptr );
mx1.setTranslation(p1);
cvf::Vec3d est_p11 = estimatedCurveCalc.firstArcEndpoint();
est_p11.transformPoint(mx1.getInverted());
CVF_ASSERT(fabs(est_p11.z()) < 1e-4 );
cvf::Mat4d mx2 = cvf::Mat4d::fromCoordSystemAxes(&t2, &est_tp2c2, nullptr );
mx2.setTranslation(p2);
cvf::Vec3d est_p22 = estimatedCurveCalc.secondArcStartpoint();
est_p22.transformPoint(mx2.getInverted());
CVF_ASSERT(fabs(est_p22.z()) < 1e-4 );
est_p_c1x = 0.0;
est_p_c1y = estimatedCurveCalc.m_r1;
est_p_p11x = est_p11.x();
est_p_p11y = est_p11.y();
est_p_c2x = 0.0;
est_p_c2y = estimatedCurveCalc.m_r2;
est_p_p22x = est_p22.x();
est_p_p22y = est_p22.y();
Slvs_MakeQuaternion(t1.x(), t1.y(), t1.z(),
est_tp1c1.x(), est_tp1c1.y(), est_tp1c1.z(),
&est_p_Plane1Qw, &est_p_Plane1Qx, &est_p_Plane1Qy, &est_p_Plane1Qz);
@ -190,7 +214,7 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
group2,
SLVS_C_PT_PT_DISTANCE,
e_Plane1,
rad1,
est_rad1,
e_P1,
e_C1,
-1,
@ -246,7 +270,7 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
// Arc2 center
Slvs_hParam p_c2x = sys.addParam(Slvs_MakeParam(-1, group2, est_p_c2x)); // Needs a better guess
Slvs_hParam p_c2x = sys.addParam(Slvs_MakeParam(-1, group2, est_p_c2x));
Slvs_hParam p_c2y = sys.addParam(Slvs_MakeParam(-1, group2, est_p_c2y));
Slvs_hEntity e_C2 = sys.addEntity(Slvs_MakePoint2d(-1, group2, e_Plane2, p_c2x, p_c2y));
@ -267,7 +291,7 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
group2,
SLVS_C_PT_PT_DISTANCE,
e_Plane2,
rad2,
est_rad2,
e_P2,
e_C2,
-1,
@ -296,7 +320,7 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
auto solveResult = sys.solve(group2, true);
if(solveResult != SolveSpaceSystem::RESULT_OKAY)
{
return;
@ -320,7 +344,7 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
e_LP11P22));
solveResult = sys.solve(group2, true);
if(solveResult != SolveSpaceSystem::RESULT_OKAY) return;
@ -336,7 +360,7 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
e_LP11P22));
solveResult = sys.solve(group2, true);
if(solveResult != SolveSpaceSystem::RESULT_OKAY) return;
@ -353,7 +377,7 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
-1));
solveResult = sys.solve(group2, true);
if(solveResult != SolveSpaceSystem::RESULT_OKAY) return;
@ -413,34 +437,92 @@ RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, double azi1, double inc1
//--------------------------------------------------------------------------------------------------
RiaSCurveCalculator::RiaSCurveCalculator(cvf::Vec3d p1, cvf::Vec3d q1,
cvf::Vec3d p2, cvf::Vec3d q2)
: m_isCalculationOK(true)
, m_p1(p1)
, m_p2(p2)
{
using Vec3d = cvf::Vec3d;
bool isOk = true;
m_isCalculationOK = true;
Vec3d tq1q2 = (q2 - q1).getNormalized(&isOk);
Vec3d tq1q2 = (q2 - q1).getNormalized(&isOk); // !ok means the control points are in the same place. Could fallback to use only one circle segment + one line.
m_isCalculationOK = m_isCalculationOK && isOk;
Vec3d t1 = (q1 - p1).getNormalized(&isOk);
Vec3d t1 = (q1 - p1).getNormalized(&isOk); // !ok means no tangent specified. Could fallback to use only one circle segment + one line.
m_isCalculationOK = m_isCalculationOK && isOk;
Vec3d t2 = (p2 - q2).getNormalized(&isOk);
Vec3d t2 = (p2 - q2).getNormalized(&isOk); // !ok means no tangent specified. Could fallback to use only one circle segment + one line or only one straight line if both tangents are missing
m_isCalculationOK = m_isCalculationOK && isOk;
Vec3d td1 = ( tq1q2 - t1).getNormalized(&isOk);
m_isCalculationOK = m_isCalculationOK && isOk;
Vec3d td2 = (-tq1q2 + t2).getNormalized(&isOk);
m_isCalculationOK = m_isCalculationOK && isOk;
{
Vec3d td1 = (tq1q2 - t1);
double td1Length = td1.length();
m_c1 = q1 + (q1 - p1).length() * (td1 * (-t1)) * td1;
m_c2 = q2 + (q2 - p2).length() * (td2 * ( t2)) * td2;
if ( td1Length > 1e-10 )
{
td1 /= td1Length;
m_c1 = q1 + ((q1 - p1).length() / (td1 * (-t1))) * td1;
m_r1 = (m_c1 - p1).length();
}
else // both control points are along t1. First curve has infinite radius
{
m_c1 = cvf::Vec3d::UNDEFINED;
m_r1 = std::numeric_limits<double>::infinity();
}
}
{
Vec3d td2 = (-tq1q2 + t2);
double td2Length = td2.length();
if ( td2Length > 1e-10 )
{
td2 /= td2Length;
m_c2 = q2 + ((q2 - p2).length() / (td2 * (t2))) * td2;
m_r2 = (m_c2 - p2).length();
}
else // both control points are along t2. Second curve has infinite radius
{
m_c2 = cvf::Vec3d::UNDEFINED;
m_r2 = std::numeric_limits<double>::infinity();
}
}
m_firstArcEndpoint = q1 + (q1 - p1).length() * tq1q2;
m_secondArcStartpoint = q2 - (q2 - p2).length() * tq1q2;
m_n1 = t1 ^ tq1q2;
m_n2 = tq1q2 ^ t2;
if (((q1 - p1).length() + (q2 - p2).length()) > (q2 - q1).length()) // first arc end and second arc start is overlapping
{
m_isCalculationOK = false;
}
// The Circle normals. Will be set to cvf::Vec3d::ZERO if undefined.
m_n1 = (t1 ^ tq1q2).getNormalized();
m_n2 = (tq1q2 ^ t2).getNormalized();
}
//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
void RiaSCurveCalculator::dump()
{
cvf::Vec3d v_C1 = firstCenter();
cvf::Vec3d v_C2 = secondCenter();
cvf::Vec3d v_N1 = firstNormal();
cvf::Vec3d v_N2 = secondNormal();
cvf::Vec3d v_P11 = firstArcEndpoint();
cvf::Vec3d v_P22 = secondArcStartpoint();
std::cout << " P1: " << "[ " << m_p1[0] << " " << m_p1[1] << " " << m_p1[2] << " " << std::endl;
std::cout << " P11: " << "[ " << v_P11[0] << " " << v_P11[1] << " " << v_P11[2] << " " << std::endl;
std::cout << " P22: " << "[ " << v_P22[0] << " " << v_P22[1] << " " << v_P22[2] << " " << std::endl;
std::cout << " P2: " << "[ " << m_p2[0] << " " << m_p2[1] << " " << m_p2[2] << " " << std::endl;
std::cout << " C1: " << "[ " << v_C1[0] << " " << v_C1[1] << " " << v_C1[2] << " " << std::endl;
std::cout << " C2: " << "[ " << v_C2[0] << " " << v_C2[1] << " " << v_C2[2] << " " << std::endl;
std::cout << " N1: " << "[ " << v_N1[0] << " " << v_N1[1] << " " << v_N1[2] << " " << std::endl;
std::cout << " N2: " << "[ " << v_N2[0] << " " << v_N2[1] << " " << v_N2[2] << " " << std::endl;
std::cout << " R1: " << "[ " << firstRadius() << " ]" << std::endl;
std::cout << " R2: " << "[ " << secondRadius() << " ]" << std::endl;
m_r1 = (m_c1 - p1).length();
m_r2 = (m_c2 - p2).length();
}
//--------------------------------------------------------------------------------------------------
@ -458,7 +540,6 @@ RiaSCurveCalculator RiaSCurveCalculator::fromTangentsAndLength(cvf::Vec3d p1, do
cvf::Vec3d Q1 = p1 + lengthToQ1 * t1;
cvf::Vec3d Q2 = p2 - lengthToQ2 * t2;
cvf::Vec3d tQ1Q2 = (Q2 - Q1).getNormalized();
RiaSCurveCalculator curveFromControlPoints(p1, Q1,
p2, Q2);

View File

@ -21,12 +21,16 @@ public:
double firstRadius() { return m_r1; }
double secondRadius() { return m_r2; }
void dump();
static RiaSCurveCalculator fromTangentsAndLength(cvf::Vec3d p1, double azi1, double inc1, double lengthToQ1,
cvf::Vec3d p2, double azi2, double inc2, double lengthToQ2 );
private:
void calculateEstimatedSolution();
bool m_isCalculationOK;
cvf::Vec3d m_p1;
cvf::Vec3d m_p2;
cvf::Vec3d m_firstArcEndpoint;
cvf::Vec3d m_secondArcStartpoint;

View File

@ -310,12 +310,14 @@ void example_S_Curve(double p1x,
std::valarray<double> v_P11 = sys.global3DPos(e_P11);
std::valarray<double> v_P22 = sys.global3DPos(e_P22);
std::cout << "C1: " << "[ " << v_C1[0] << ", " << v_C1[1] << ", " << v_C1[2] << " ]" << std::endl;
std::cout << "N1: " << "[ " << v_N1[0] << ", " << v_N1[1] << ", " << v_N1[2] << " ]" << std::endl;
std::cout << "P11: " << "[ " << v_P11[0] << ", " << v_P11[1] << ", " << v_P11[2] << " ]" << std::endl;
std::cout << "C2: " << "[ " << v_C2[0] << ", " << v_C2[1] << ", " << v_C2[2] << " ]" << std::endl;
std::cout << "N1: " << "[ " << v_N2[0] << ", " << v_N2[1] << ", " << v_N2[2] << " ]" << std::endl;
std::cout << "P22: " << "[ " << v_P22[0] << ", " << v_P22[1] << ", " << v_P22[2] << " ]" << std::endl;
std::cout << "P1: " << "[ " << p1x << " " << p1y << " " << p1z << " " << std::endl;
std::cout << "P11: " << "[ " << v_P11[0] << " " << v_P11[1] << " " << v_P11[2] << " " << std::endl;
std::cout << "P22: " << "[ " << v_P22[0] << " " << v_P22[1] << " " << v_P22[2] << " " << std::endl;
std::cout << "P2: " << "[ " << p2x << " " << p2y << " " << p2z << " " << std::endl;
std::cout << "C1: " << "[ " << v_C1[0] << " " << v_C1[1] << " " << v_C1[2] << " " << std::endl;
std::cout << "C2: " << "[ " << v_C2[0] << " " << v_C2[1] << " " << v_C2[2] << " " << std::endl;
std::cout << "N1: " << "[ " << v_N1[0] << " " << v_N1[1] << " " << v_N1[2] << " " << std::endl;
std::cout << "N2: " << "[ " << v_N2[0] << " " << v_N2[1] << " " << v_N2[2] << " " << std::endl;
}
@ -324,7 +326,7 @@ void example_S_Curve(double p1x,
//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
TEST(DISABLED_SolveSpaceSolverTest, SCurve)
TEST(SolveSpaceSolverTest, SCurve)
{
example_S_Curve(100, 100, 0, 0, M_PI/4, 12,
100, 150, -1000, M_PI, M_PI/4, 12);
@ -335,7 +337,7 @@ TEST(DISABLED_SolveSpaceSolverTest, SCurve)
//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
TEST(DISABLED_RiaSCurveCalculator, Test1)
TEST(RiaSCurveCalculator, Test1)
{
RiaSCurveCalculator sCurveCalc({ 100, 100, 0 },
@ -347,23 +349,31 @@ TEST(DISABLED_RiaSCurveCalculator, Test1)
M_PI/4,
12);
EXPECT_TRUE(sCurveCalc.isOk() );
cvf::Vec3d v_C1 = sCurveCalc.firstCenter();
cvf::Vec3d v_C2 = sCurveCalc.secondCenter();
cvf::Vec3d v_N1 = sCurveCalc.firstNormal();
cvf::Vec3d v_N2 = sCurveCalc.secondNormal();
cvf::Vec3d v_P11 = sCurveCalc.firstArcEndpoint();
cvf::Vec3d v_P22 = sCurveCalc.secondArcStartpoint();
std::cout << "C1: " << "[ " << v_C1[0] << ", " << v_C1[1] << ", " << v_C1[2] << " ]" << std::endl;
std::cout << "N1: " << "[ " << v_N1[0] << ", " << v_N1[1] << ", " << v_N1[2] << " ]" << std::endl;
std::cout << "P11: " << "[ " << v_P11[0] << ", " << v_P11[1] << ", " << v_P11[2] << " ]" << std::endl;
std::cout << "C2: " << "[ " << v_C2[0] << ", " << v_C2[1] << ", " << v_C2[2] << " ]" << std::endl;
std::cout << "N1: " << "[ " << v_N2[0] << ", " << v_N2[1] << ", " << v_N2[2] << " ]" << std::endl;
std::cout << "P22: " << "[ " << v_P22[0] << ", " << v_P22[1] << ", " << v_P22[2] << " ]" << std::endl;
sCurveCalc.dump();
}
TEST(DISABLED_RiaSCurveCalculator, Test2)
//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
TEST(RiaSCurveCalculator, Test1AtEstimate)
{
RiaSCurveCalculator sCurveCalc({ 100, 100, 0 },
0,
M_PI/4,
535.452,
{ 100, 150, -1000 },
M_PI,
M_PI/4,
439.508);
EXPECT_TRUE(sCurveCalc.isOk() );
sCurveCalc.dump();
}
TEST(RiaSCurveCalculator, Test2)
{
RiaSCurveCalculator sCurveCalc({ 100, 100, 0 },
0,
@ -376,23 +386,12 @@ TEST(DISABLED_RiaSCurveCalculator, Test2)
EXPECT_TRUE(sCurveCalc.isOk());
cvf::Vec3d v_C1 = sCurveCalc.firstCenter();
cvf::Vec3d v_C2 = sCurveCalc.secondCenter();
cvf::Vec3d v_N1 = sCurveCalc.firstNormal();
cvf::Vec3d v_N2 = sCurveCalc.secondNormal();
cvf::Vec3d v_P11 = sCurveCalc.firstArcEndpoint();
cvf::Vec3d v_P22 = sCurveCalc.secondArcStartpoint();
sCurveCalc.dump();
std::cout << "C1: " << "[ " << v_C1[0] << ", " << v_C1[1] << ", " << v_C1[2] << " ]" << std::endl;
std::cout << "N1: " << "[ " << v_N1[0] << ", " << v_N1[1] << ", " << v_N1[2] << " ]" << std::endl;
std::cout << "P11: " << "[ " << v_P11[0] << ", " << v_P11[1] << ", " << v_P11[2] << " ]" << std::endl;
std::cout << "C2: " << "[ " << v_C2[0] << ", " << v_C2[1] << ", " << v_C2[2] << " ]" << std::endl;
std::cout << "N1: " << "[ " << v_N2[0] << ", " << v_N2[1] << ", " << v_N2[2] << " ]" << std::endl;
std::cout << "P22: " << "[ " << v_P22[0] << ", " << v_P22[1] << ", " << v_P22[2] << " ]" << std::endl;
}
TEST(DISABLED_RiaSCurveCalculator, Test3)
TEST(RiaSCurveCalculator, Test3)
{
RiaSCurveCalculator sCurveCalc({ 100, 100, 0 },
0,
@ -405,17 +404,172 @@ TEST(DISABLED_RiaSCurveCalculator, Test3)
EXPECT_TRUE(sCurveCalc.isOk() );
cvf::Vec3d v_C1 = sCurveCalc.firstCenter();
cvf::Vec3d v_C2 = sCurveCalc.secondCenter();
cvf::Vec3d v_N1 = sCurveCalc.firstNormal();
cvf::Vec3d v_N2 = sCurveCalc.secondNormal();
cvf::Vec3d v_P11 = sCurveCalc.firstArcEndpoint();
cvf::Vec3d v_P22 = sCurveCalc.secondArcStartpoint();
sCurveCalc.dump();
}
void printQ1Q2R1R2Matrix(cvf::Vec3d p1, double azi1, double inc1,
cvf::Vec3d p2, double azi2, double inc2)
{
double q1Start = 0.0;
double q1End = 3000;
double step1 = 100;
double q2Start = 0.0;
double q2End = 3000;
double step2 = 100;
std::cout << "R1" << std::endl;
std::cout << "q1\\q2" << " ";
for (double q2 = q2Start; q2 < q2End; q2 += step2)
{
std::cout << q2 << " ";
}
std::cout << std::endl;
for (double q1 = q1Start; q1 < q1End; q1 += step1)
{
std::cout << q1 << " ";
for (double q2 = q2Start; q2 < q2End; q2 += step2)
{
RiaSCurveCalculator sCurveCalc = RiaSCurveCalculator::fromTangentsAndLength(p1, azi1, inc1, q1,
p2, azi2, inc2, q2);
if ( sCurveCalc.isOk() )
{
std::cout << sCurveCalc.firstRadius() << " " ;
}
else
{
std::cout << "NS" << " " ;
}
}
std::cout << std::endl;
}
std::cout << std::endl;
std::cout << "R2" << std::endl;
std::cout << "q1\\q2" << " ";
for (double q2 = q2Start; q2 < q2End; q2 += step2)
{
std::cout << q2 << " ";
}
std::cout << std::endl;
for (double q1 = q1Start; q1 < q1End; q1 += step1)
{
std::cout << q1 << " ";
for (double q2 = q2Start; q2 < q2End; q2 += step2)
{
RiaSCurveCalculator sCurveCalc = RiaSCurveCalculator::fromTangentsAndLength(p1, azi1, inc1, q1,
p2, azi2, inc2, q2);
if ( sCurveCalc.isOk() )
{
std::cout << sCurveCalc.secondRadius() << " " ;
}
else
{
std::cout << "NS" << " " ;
}
}
std::cout << std::endl;
}
}
TEST(DISABLED_RiaSCurveCalculator, q_r_relation)
{
std::cout << "Config 1" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, 0,
{ 0,0,-1000 }, 0, 0);
std::cout << "Config 1a" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, 0,
{ 0,0,-1000 }, 0, 0.01);
std::cout << "Config 2" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, 0,
{ 0,0,-1000 }, 0, M_PI/2.0);
std::cout << "Config 3" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, 0,
{ 0,0,-1000 }, 0, M_PI);
std::cout << "Config 3a" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, 0,
{ 0,0,-1000 }, 0, M_PI-0.01);
std::cout << "Config 4" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI/2.0,
{ 0,0,-1000 }, 0, M_PI/2.0);
std::cout << "Config 5" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI/2.0,
{ 0,0,-1000 }, M_PI, M_PI/2.0);
std::cout << "Config 6" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI,
{ 0,0,-1000 }, 0, 0);
std::cout << "Config 6a" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI,
{ 0,0,-1000 }, 0, 0.01);
std::cout << "Config 6b" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI-0.01,
{ 0,0,-1000 }, 0, 0.00);
std::cout << "Config 7" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI,
{ 0,0,-1000 }, 0, M_PI/2.0);
std::cout << "Config 8" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI,
{ 0,0,-1000 }, 0, M_PI);
std::cout << "Config 8a" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI,
{ 0,0,-1000 }, 0, M_PI-0.01);
std::cout << "Config 8b" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI-0.01,
{ 0,0,-1000 }, 0, M_PI);
std::cout << "Config 9" << std::endl;
printQ1Q2R1R2Matrix(
{ 0,0,0 }, 0, M_PI/2,
{ 0,0,-1000 }, M_PI/2, M_PI/2);
std::cout << "C1: " << "[ " << v_C1[0] << ", " << v_C1[1] << ", " << v_C1[2] << " ]" << std::endl;
std::cout << "N1: " << "[ " << v_N1[0] << ", " << v_N1[1] << ", " << v_N1[2] << " ]" << std::endl;
std::cout << "P11: " << "[ " << v_P11[0] << ", " << v_P11[1] << ", " << v_P11[2] << " ]" << std::endl;
std::cout << "C2: " << "[ " << v_C2[0] << ", " << v_C2[1] << ", " << v_C2[2] << " ]" << std::endl;
std::cout << "N1: " << "[ " << v_N2[0] << ", " << v_N2[1] << ", " << v_N2[2] << " ]" << std::endl;
std::cout << "P22: " << "[ " << v_P22[0] << ", " << v_P22[1] << ", " << v_P22[2] << " ]" << std::endl;
}