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irrlicht/tests/matrixOps.cpp
cutealien 3f372af486 Fix some problems with CMatrix4::getRotationDegrees 
- Only the getRotationDegrees without parameter is allowed to try fixing scale.
  My fault when I added a new function which takes scale parameter, that one is 
  not allowed to be changed.
  On the up-side - we know have for the first time an option which works in cases only
  scale and rotation had been used and the user still has the correct scale. 
  Before any solution for that was broken
- getRotationDegrees fixes 2 places which caused wrong results due to floating point inaccuracies
  New test for that got added
- Document the current restrains and problems of getRotationDegrees and getScale some more.
- Improve docs for other matrix4 functions.
- Add some comments about further improvements (I'll try if I find time)

Note: Irrlicht still assumes in at least 2 places (getting bone animations and Collada loader) that matrix
decomposing works. Which it doesn't yet for matrices which switch handedness (or have further transformations like skewing axes)
The bone animation is mostly fine for now with recent workaround (but that might cause other problems as it may be used too often), haven't checked Collada yet in detail.

TL/DR: This improves things with getRotationDegrees, but does not yet fix all troubles.


git-svn-id: svn://svn.code.sf.net/p/irrlicht/code/trunk@6439 dfc29bdd-3216-0410-991c-e03cc46cb475
2022-10-15 15:46:03 +00:00

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// Copyright (C) 2008-2012 Colin MacDonald
// No rights reserved: this software is in the public domain.
#include "testUtils.h"
using namespace irr;
using namespace core;
using namespace scene;
using namespace video;
using namespace io;
using namespace gui;
namespace
{
// Basic tests for identity matrix
bool identity(void)
{
bool result = true;
matrix4 m;
// Check default init
result &= (m==core::IdentityMatrix);
result &= (core::IdentityMatrix==m);
assert_log(result);
// Since the last test can be made with isDefinitelyIdentityMatrix we set it to false here
m.setDefinitelyIdentityMatrix(false);
result &= (m==core::IdentityMatrix);
result &= (core::IdentityMatrix==m);
assert_log(result);
// also equals should see this
result &= m.equals(core::IdentityMatrix);
result &= core::IdentityMatrix.equals(m);
assert_log(result);
// Check inequality
m[12]=5.f;
result &= (m!=core::IdentityMatrix);
result &= (core::IdentityMatrix!=m);
result &= !m.equals(core::IdentityMatrix);
result &= !core::IdentityMatrix.equals(m);
assert_log(result);
// Test multiplication
result &= (m==(core::IdentityMatrix*m));
result &= m.equals(core::IdentityMatrix*m);
result &= (m==(m*core::IdentityMatrix));
result &= m.equals(m*core::IdentityMatrix);
assert_log(result);
return result;
}
// Test rotations
bool transformations(void)
{
bool result = true;
matrix4 m, s;
m.setRotationDegrees(core::vector3df(30,40,50));
s.setScale(core::vector3df(2,3,4));
m *= s;
m.setTranslation(core::vector3df(5,6,7));
result &= (core::vector3df(5,6,7).equals(m.getTranslation()));
assert_log(result);
result &= (core::vector3df(2,3,4).equals(m.getScale()));
assert_log(result);
core::vector3df newRotation = m.getRotationDegrees();
result &= (core::vector3df(30,40,50).equals(newRotation, 0.000004f));
assert_log(result);
m.setRotationDegrees(vector3df(90.0001f, 270.85f, 180.0f));
s.setRotationDegrees(vector3df(0,0, 0.860866f));
m *= s;
newRotation = m.getRotationDegrees();
result &= (core::vector3df(0,270,270).equals(newRotation, 0.0001f));
assert_log(result);
m.setRotationDegrees(vector3df(270.0f, 89.8264f, 0.000100879f));
s.setRotationDegrees(vector3df(0,0, 0.189398f));
m *= s;
newRotation = m.getRotationDegrees();
result &= (core::vector3df(0,90,90).equals(newRotation, 0.0001f));
assert_log(result);
m.setRotationDegrees(vector3df(270.0f, 89.0602f, 359.999f));
s.setRotationDegrees(vector3df(0,0, 0.949104f));
m *= s;
newRotation = m.getRotationDegrees();
result &= (core::vector3df(0,90,89.999f).equals(newRotation));
assert_log(result);
return result;
}
// Test rotations
bool rotations(void)
{
bool result = true;
matrix4 rot1,rot2,rot3,rot4,rot5;
core::vector3df vec1(1,2,3),vec12(1,2,3);
core::vector3df vec2(-5,0,0),vec22(-5,0,0);
core::vector3df vec3(20,0,-20), vec32(20,0,-20);
// Make sure the matrix multiplication and rotation application give same results
rot1.setRotationDegrees(core::vector3df(90,0,0));
rot2.setRotationDegrees(core::vector3df(0,90,0));
rot3.setRotationDegrees(core::vector3df(0,0,90));
rot4.setRotationDegrees(core::vector3df(90,90,90));
rot5 = rot3*rot2*rot1;
result &= (rot4.equals(rot5, ROUNDING_ERROR_f32));
assert_log(result);
rot4.transformVect(vec1);rot5.transformVect(vec12);
rot4.transformVect(vec2);rot5.transformVect(vec22);
rot4.transformVect(vec3);rot5.transformVect(vec32);
result &= (vec1.equals(vec12));
result &= (vec2.equals(vec22));
result &= (vec3.equals(vec32));
assert_log(result);
vec1.set(1,2,3);vec12.set(1,2,3);
vec2.set(-5,0,0);vec22.set(-5,0,0);
vec3.set(20,0,-20);vec32.set(20,0,-20);
rot1.setRotationDegrees(core::vector3df(45,0,0));
rot2.setRotationDegrees(core::vector3df(0,45,0));
rot3.setRotationDegrees(core::vector3df(0,0,45));
rot4.setRotationDegrees(core::vector3df(45,45,45));
rot5 = rot3*rot2*rot1;
result &= (rot4.equals(rot5, ROUNDING_ERROR_f32));
assert_log(result);
rot4.transformVect(vec1);rot5.transformVect(vec12);
rot4.transformVect(vec2);rot5.transformVect(vec22);
rot4.transformVect(vec3);rot5.transformVect(vec32);
result &= (vec1.equals(vec12));
result &= (vec2.equals(vec22));
result &= (vec3.equals(vec32, 2*ROUNDING_ERROR_f32));
assert_log(result);
vec1.set(1,2,3);vec12.set(1,2,3);
vec2.set(-5,0,0);vec22.set(-5,0,0);
vec3.set(20,0,-20);vec32.set(20,0,-20);
rot1.setRotationDegrees(core::vector3df(-60,0,0));
rot2.setRotationDegrees(core::vector3df(0,-60,0));
rot3.setRotationDegrees(core::vector3df(0,0,-60));
rot4.setRotationDegrees(core::vector3df(-60,-60,-60));
rot5 = rot3*rot2*rot1;
result &= (rot4.equals(rot5, ROUNDING_ERROR_f32));
assert_log(result);
rot4.transformVect(vec1);rot5.transformVect(vec12);
rot4.transformVect(vec2);rot5.transformVect(vec22);
rot4.transformVect(vec3);rot5.transformVect(vec32);
result &= (vec1.equals(vec12));
result &= (vec2.equals(vec22));
// this one needs higher tolerance due to rounding issues
result &= (vec3.equals(vec32, 0.000002f));
assert_log(result);
vec1.set(1,2,3);vec12.set(1,2,3);
vec2.set(-5,0,0);vec22.set(-5,0,0);
vec3.set(20,0,-20);vec32.set(20,0,-20);
rot1.setRotationDegrees(core::vector3df(113,0,0));
rot2.setRotationDegrees(core::vector3df(0,-27,0));
rot3.setRotationDegrees(core::vector3df(0,0,193));
rot4.setRotationDegrees(core::vector3df(113,-27,193));
rot5 = rot3*rot2*rot1;
result &= (rot4.equals(rot5, ROUNDING_ERROR_f32));
assert_log(result);
rot4.transformVect(vec1);rot5.transformVect(vec12);
rot4.transformVect(vec2);rot5.transformVect(vec22);
rot4.transformVect(vec3);rot5.transformVect(vec32);
// these ones need higher tolerance due to rounding issues
result &= (vec1.equals(vec12, 0.000002f));
assert_log(result);
result &= (vec2.equals(vec22));
assert_log(result);
result &= (vec3.equals(vec32, 0.000002f));
assert_log(result);
rot1.setRotationDegrees(core::vector3df(0,0,34));
rot2.setRotationDegrees(core::vector3df(0,43,0));
vec1=(rot2*rot1).getRotationDegrees();
result &= (vec1.equals(core::vector3df(27.5400505f, 34.4302292f, 42.6845398f), 0.000002f));
assert_log(result);
// corner cases
rot1.setRotationDegrees(irr::core::vector3df(180.0f, 0.f, 0.f));
vec1=rot1.getRotationDegrees();
result &= (vec1.equals(core::vector3df(180.0f, 0.f, 0.f), 0.000002f));
assert_log(result);
rot1.setRotationDegrees(irr::core::vector3df(0.f, 180.0f, 0.f));
vec1=rot1.getRotationDegrees();
result &= (vec1.equals(core::vector3df(180.0f, 360, 180.0f), 0.000002f));
assert_log(result);
rot1.setRotationDegrees(irr::core::vector3df(0.f, 0.f, 180.0f));
vec1=rot1.getRotationDegrees();
result &= (vec1.equals(core::vector3df(0.f, 0.f, 180.0f), 0.000002f));
assert_log(result);
rot1.makeIdentity();
rot1.setRotationDegrees(core::vector3df(270.f,0,0));
rot2.makeIdentity();
rot2.setRotationDegrees(core::vector3df(-90.f,0,0));
vec1=(rot1*rot2).getRotationDegrees();
result &= (vec1.equals(core::vector3df(180.f, 0.f, 0.0f)));
assert_log(result);
return result;
}
// Test isOrthogonal
bool isOrthogonal(void)
{
matrix4 rotationMatrix;
if (!rotationMatrix.isOrthogonal())
{
logTestString("irr::core::matrix4::isOrthogonal() failed with Identity.\n");
return false;
}
rotationMatrix.setRotationDegrees(vector3df(90, 0, 0));
if (!rotationMatrix.isOrthogonal())
{
logTestString("irr::core::matrix4::isOrthogonal() failed with rotation.\n");
return false;
}
matrix4 translationMatrix;
translationMatrix.setTranslation(vector3df(0, 3, 0));
if (translationMatrix.isOrthogonal())
{
logTestString("irr::core::matrix4::isOrthogonal() failed with translation.\n");
return false;
}
matrix4 scaleMatrix;
scaleMatrix.setScale(vector3df(1, 2, 3));
if (!scaleMatrix.isOrthogonal())
{
logTestString("irr::core::matrix4::isOrthogonal() failed with scale.\n");
return false;
}
return true;
}
bool checkMatrixRotation(irr::core::matrix4& m, const vector3df& vector, const vector3df& expectedResult)
{
vector3df v(vector);
m.rotateVect(v);
if ( expectedResult.equals(v) )
return true;
logTestString("checkMatrixRotation failed for vector %f %f %f. Expected %f %f %f, got %f %f %f \n"
, vector.X, vector.Y, vector.Z, expectedResult.X, expectedResult.Y, expectedResult.Z, v.X, v.Y, v.Z);
logTestString("matrix: ");
for ( int i=0; i<16; ++i )
logTestString("%.2f ", m[i]);
logTestString("\n");
return false;
}
bool setRotationAxis()
{
matrix4 m;
vector3df v;
// y up, x right, z depth (as usual)
// y rotated around x-axis
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(1,0,0)), vector3df(0,1,0), vector3df(0, 0, 1)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
if ( !checkMatrixRotation( m.setRotationAxisRadians(180.f*DEGTORAD, vector3df(1,0,0)), vector3df(0,1,0), vector3df(0, -1, 0)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
// y rotated around negative x-axis
m.makeIdentity();
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(-1,0,0)), vector3df(0,1,0), vector3df(0, 0, -1)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
// x rotated around x-axis
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(1,0,0)), vector3df(1,0,0), vector3df(1, 0, 0)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
// x rotated around y-axis
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(0,1,0)), vector3df(1,0,0), vector3df(0, 0, -1)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
if ( !checkMatrixRotation( m.setRotationAxisRadians(180.f*DEGTORAD, vector3df(0,1,0)), vector3df(1,0,0), vector3df(-1, 0, 0)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
// x rotated around negative y-axis
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(0,-1,0)), vector3df(1,0,0), vector3df(0, 0, 1)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
// y rotated around y-axis
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(0,1,0)), vector3df(0,1,0), vector3df(0, 1, 0)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
// x rotated around z-axis
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(0,0,1)), vector3df(1,0,0), vector3df(0, 1, 0)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
if ( !checkMatrixRotation( m.setRotationAxisRadians(180.f*DEGTORAD, vector3df(0,0,1)), vector3df(1,0,0), vector3df(-1, 0, 0)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
// x rotated around negative z-axis
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(0,0,-1)), vector3df(1,0,0), vector3df(0, -1, 0)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
// y rotated around z-axis
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(0,0,1)), vector3df(0,1,0), vector3df(-1, 0, 0)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
if ( !checkMatrixRotation( m.setRotationAxisRadians(180.f*DEGTORAD, vector3df(0,0,1)), vector3df(0,1,0), vector3df(0, -1, 0)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
// z rotated around z-axis
if ( !checkMatrixRotation( m.setRotationAxisRadians(90.f*DEGTORAD, vector3df(0,0,1)), vector3df(0,0,1), vector3df(0, 0, 1)) )
{
logTestString("%s:%d", __FILE__, __LINE__);
return false;
}
return true;
}
// Note: pretty high tolerance needed
bool check_getRotationDegreesWithScale2(const core::matrix4& m, const irr::core::vector3df& scale, irr::f32 tolerance = 0.01f)
{
core::vector3df rot = m.getRotationDegrees(scale);
core::matrix4 m2;
m2.setRotationDegrees(rot);
core::matrix4 smat;
smat.setScale(scale);
m2 *= smat;
core::vector3df v1(5,10,15);
core::vector3df v2 = v1;
m.transformVect(v1);
m2.transformVect(v2);
if ( v1.equals(v2, tolerance) )
return true;
logTestString("v1: %.3f %.3f %.3f\nv2: %.3f %.3f %.3f\n", v1.X, v1.Y, v1.Z, v2.X, v2.Y, v2.Z);
//logTestString("matrix (3x3): ");
//for ( int k=0; k<3; ++k)
// for ( int i=0; i<3; ++i )
// logTestString("%.3f ", m[k*4+i]);
//logTestString("\n");
return false;
}
// This can only work if the matrix is pure scale or pure rotation
bool check_getRotationDegreesWithScale(const core::matrix4& m, irr::f32 tolerance = 0.001f)
{
core::vector3df scale = m.getScale();
return check_getRotationDegreesWithScale2(m, scale, tolerance);
}
// Lazy macro only to be used inside the loop where it is used
// (can't use lambda yet, still testing on older compilers)
#define log_check_getRotationDegreesWithScaleIJK \
do { \
smat.setScale(scale); \
m2 = m1*smat; \
if ( !check_getRotationDegreesWithScale2(m2, scale) ) { \
logTestString("%s:%d i:%f j:%f k:%f\n", __FILE__, __LINE__, i, j, k); \
result = false; } \
} while (false)
bool decompose()
{
bool result = true;
core::matrix4 m1;
result &= check_getRotationDegreesWithScale(m1);
// check pure scaling/90<39> rotations and 0 values
for ( irr::f32 i = -2.f; i <= 2.f; i += 1.f )
for ( irr::f32 j = -2.f; j <= 2.f; j += 1.f )
for ( irr::f32 k = -2.f; k <= 2.f; k += 1.f )
{
m1 = core::matrix4();
m1[0] = i;
m1[5] = j;
m1[10] = k;
if ( !check_getRotationDegreesWithScale(m1) )
{
logTestString("%s:%d i:%f j:%f k:%f\n", __FILE__, __LINE__, i, j, k);
result = false;
}
}
// check some rotations (note that we avoid the 0 case - which won't work)
for ( irr::f32 i = -180.f; i <= 360.f; i += 30.1f )
for ( irr::f32 j = -120.f; j <= 200.f; j += 44.4f )
for ( irr::f32 k = -10.f; k <= 180.f; k += 33.3f )
{
m1 = core::matrix4();
m1.setRotationDegrees(core::vector3df(i,j,k));
result &= check_getRotationDegreesWithScale(m1); // pure rotation
// rotation + scaling tests
// We can't use check_getRotationDegreesWithScale as we have no way so far to decompose a combined matrix
core::matrix4 smat, m2;
core::vector3df scale;
scale = core::vector3df(2.f, 2.f, 2.f); // simple uniform scaling
log_check_getRotationDegreesWithScaleIJK;
scale = core::vector3df(-2.f, 2.f, 2.f); // simple uniform scaling which swaps handedness
log_check_getRotationDegreesWithScaleIJK; // (TODO: can't decompose this yet)
scale = core::vector3df(i, i, i); // flexible uniform scaling
log_check_getRotationDegreesWithScaleIJK; // (TODO: can't decompose this yet)
scale = core::vector3df(1, 2, 3); // simple non-uniform scaling
log_check_getRotationDegreesWithScaleIJK;
scale = core::vector3df(-1, -2, -3); // negative non-uniform scaling with swap of handedness
log_check_getRotationDegreesWithScaleIJK; // (TODO: can't decompose this yet)
scale = core::vector3df(-1, 2, -3); // +- non-uniform scaling
log_check_getRotationDegreesWithScaleIJK;
scale = core::vector3df(i,k,j); // non-uniform scaling
log_check_getRotationDegreesWithScaleIJK; // (TODO: can't decompose this yet)
}
if ( !result )
logTestString("decomposing matrix failed\n");
return result;
}
// just calling each function once to find compile problems
void calltest()
{
matrix4 mat;
matrix4 mat2(mat);
f32& f1 = mat(0,0);
const f32& f2 = mat(0,0);
f32& f3 = mat[0];
const f32& f4 = mat[0];
mat = mat;
mat = 1.f;
const f32 * pf1 = mat.pointer();
f32 * pf2 = mat.pointer();
bool b = mat == mat2;
b = mat != mat2;
mat = mat + mat2;
mat += mat2;
mat = mat - mat2;
mat -= mat2;
mat.setbyproduct(mat, mat2);
mat.setbyproduct_nocheck(mat, mat2);
mat = mat * mat2;
mat *= mat2;
mat = mat * 10.f;
mat *= 10.f;
mat.makeIdentity();
b = mat.isIdentity();
b = mat.isOrthogonal();
b = mat.isIdentity_integer_base ();
mat.setTranslation(vector3df(1.f, 1.f, 1.f) );
vector3df v1 = mat.getTranslation();
mat.setInverseTranslation(vector3df(1.f, 1.f, 1.f) );
mat.setRotationRadians(vector3df(1.f, 1.f, 1.f) );
mat.setRotationDegrees(vector3df(1.f, 1.f, 1.f) );
vector3df v2 = mat.getRotationDegrees();
mat.setInverseRotationRadians(vector3df(1.f, 1.f, 1.f) );
mat.setInverseRotationDegrees(vector3df(1.f, 1.f, 1.f) );
mat.setRotationAxisRadians(1.f, vector3df(1.f, 1.f, 1.f) );
mat.setScale(vector3df(1.f, 1.f, 1.f) );
mat.setScale(1.f);
vector3df v3 = mat.getScale();
mat.inverseTranslateVect(v1);
mat.inverseRotateVect(v1);
mat.rotateVect(v1);
mat.rotateVect(v1, v2);
f32 fv3[3];
mat.rotateVect(fv3, v1);
mat.transformVect(v1);
mat.transformVect(v1, v1);
f32 fv4[4];
mat.transformVect(fv4, v1);
mat.transformVec3(fv3, fv3);
mat.translateVect(v1);
plane3df p1;
mat.transformPlane(p1);
mat.transformPlane(p1, p1);
aabbox3df bb1;
mat.transformBox(bb1);
mat.transformBoxEx(bb1);
mat.multiplyWith1x4Matrix(fv4);
mat.makeInverse();
b = mat.getInversePrimitive(mat2);
b = mat.getInverse(mat2);
mat.buildProjectionMatrixPerspectiveFovRH(1.f, 1.f, 1.f, 1000.f);
mat.buildProjectionMatrixPerspectiveFovLH(1.f, 1.f, 1.f, 1000.f);
mat.buildProjectionMatrixPerspectiveFovInfinityLH(1.f, 1.f, 1.f);
mat.buildProjectionMatrixPerspectiveRH(100.f, 100.f, 1.f, 1000.f);
mat.buildProjectionMatrixPerspectiveLH(10000.f, 10000.f, 1.f, 1000.f);
mat.buildProjectionMatrixOrthoLH(10000.f, 10000.f, 1.f, 1000.f);
mat.buildProjectionMatrixOrthoRH(10000.f, 10000.f, 1.f, 1000.f);
mat.buildCameraLookAtMatrixLH(vector3df(1.f, 1.f, 1.f), vector3df(0.f, 0.f, 0.f), vector3df(0.f, 1.f, 0.f) );
mat.buildCameraLookAtMatrixRH(vector3df(1.f, 1.f, 1.f), vector3df(0.f, 0.f, 0.f), vector3df(0.f, 1.f, 0.f) );
mat.buildShadowMatrix(vector3df(1.f, 1.f, 1.f), p1);
core::rect<s32> a1(0,0,100,100);
mat.buildNDCToDCMatrix(a1, 1.f);
mat.interpolate(mat2, 1.f);
mat = mat.getTransposed();
mat.getTransposed(mat2);
mat.buildRotateFromTo(vector3df(1.f, 1.f, 1.f), vector3df(1.f, 1.f, 1.f));
mat.setRotationCenter(vector3df(1.f, 1.f, 1.f), vector3df(1.f, 1.f, 1.f));
mat.buildAxisAlignedBillboard(vector3df(1.f, 1.f, 1.f), vector3df(1.f, 1.f, 1.f), vector3df(1.f, 1.f, 1.f), vector3df(1.f, 1.f, 1.f), vector3df(1.f, 1.f, 1.f));
mat.buildTextureTransform( 1.f,vector2df(1.f, 1.f), vector2df(1.f, 1.f), vector2df(1.f, 1.f));
mat.setTextureRotationCenter( 1.f );
mat.setTextureTranslate( 1.f, 1.f );
mat.setTextureTranslateTransposed(1.f, 1.f);
mat.setTextureScale( 1.f, 1.f );
mat.setTextureScaleCenter( 1.f, 1.f );
f32 fv16[16];
mat.setM(fv16);
mat.setDefinitelyIdentityMatrix(false);
b = mat.getDefinitelyIdentityMatrix();
b = mat.equals(mat2);
f1 = f1+f2+f3+f4+*pf1+*pf2; // getting rid of unused variable warnings.
}
}
bool matrixOps(void)
{
bool result = true;
calltest();
result &= identity();
result &= rotations();
result &= isOrthogonal();
result &= transformations();
result &= setRotationAxis();
result &= decompose();
return result;
}
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