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// -*- compile-command: "./test_single_testcase.sh TTestCastleQuaternions" -*-
{
Copyright 2018-2023 Michalis Kamburelis.
This file is part of "Castle Game Engine".
"Castle Game Engine" is free software; see the file COPYING.txt,
included in this distribution, for details about the copyright.
"Castle Game Engine" is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
----------------------------------------------------------------------------
}
{ Tests of CastleQuaternions unit. }
unit TestCastleQuaternions;
interface
uses
Classes, SysUtils,
CastleTester, CastleVectors, CastleQuaternions;
type
TTestCastleQuaternions = class(TCastleTestCase)
published
procedure TestRotationMatrix;
procedure TestDecompose;
procedure TestDecomposeCastleTransform;
procedure TestSlerpEpsilon;
end;
implementation
uses CastleTransform;
procedure TTestCastleQuaternions.TestRotationMatrix;
var
NewQ, Q: TQuaternion;
M: TMatrix3;
begin
Q := QuatFromAxisAngle(Vector3(1, 2, 3), 6.666, true);
M := Q.ToRotationMatrix3;
NewQ := QuatFromRotationMatrix(M);
// Writeln(Q.Data.Vector4.ToString);
// Writeln(NewQ.Data.Vector4.ToString);
// Writeln(Q.ToAxisAngle.ToString);
// Writeln(NewQ.ToAxisAngle.ToString);
// Writeln(Q.Rotate(Vector3(30, 20, 10)).ToString);
// Writeln(NewQ.Rotate(Vector3(30, 20, 10)).ToString);
{ easy way to check that quaternions are equal: check that they rotate
some point in the same way. }
AssertVectorEquals(
Q.Rotate(Vector3(30, 20, 10)),
NewQ.Rotate(Vector3(30, 20, 10)));
end;
procedure TTestCastleQuaternions.TestDecompose;
var
M: TMatrix4;
Translation, Scale: TVector3;
Rotation: TVector4;
begin
{ The order is the same as for @link(TTransformation,Multiply),
and same as done by TCastleTransform: first translation matrix,
multiplied by rotation matrix,
multiplied by scaling matrix. }
M := TranslationMatrix(Vector3(44, 100, 200)) *
RotationMatrixRad(6.66, Vector3(1, 2, 3).Normalize) *
ScalingMatrix(Vector3(9, 8, 7));
MatrixDecompose(M, Translation, Rotation, Scale);
AssertVectorEquals(Translation, Vector3(44, 100, 200), 0.1);
AssertVectorEquals(Rotation.XYZ, Vector3(1, 2, 3).Normalize, 0.1);
AssertVectorEquals(Scale, Vector3(9, 8, 7), 0.1);
// Writeln(Translation.ToString);
// Writeln(Rotation.ToString);
// Writeln(Scale.ToString);
end;
procedure TTestCastleQuaternions.TestDecomposeCastleTransform;
var
M: TMatrix4;
Translation, Scale: TVector3;
Rotation: TVector4;
Transform: TCastleTransform;
begin
M :=
TranslationMatrix(Vector3(1, 2, 3)) *
RotationMatrixRad(6.66, Vector3(5, 6, 7).Normalize) *
ScalingMatrix(Vector3(9, 8, 7)) *
TranslationMatrix(Vector3(10, 20, 30)) *
RotationMatrixRad(6.66, Vector3(50, 60, 70).Normalize) *
ScalingMatrix(Vector3(9, 8, 7));
MatrixDecompose(M, Translation, Rotation, Scale);
Transform := TCastleTransform.Create(nil);
try
Transform.Translation := Translation;
Transform.Rotation := Rotation;
Transform.Scale := Scale;
AssertMatrixEquals(Transform.Transform, M, 5);
finally FreeAndNil(Transform) end;
end;
procedure TTestCastleQuaternions.TestSlerpEpsilon;
{ For some particular inputs, SLerp could calculate wrong results if the Epsilon in SLerp
will be too large. Below are invalid calculations (with Epsilon = 1E-3)
vs valid (Epsilon = 1E-6) on glTF model from https://github.com/castle-engine/castle-engine/issues/342 .
SinTheta 0.00048828122090000000
A 0.19590963423252106
-0.49971881508827209 -0.49972546100616455 -0.50027436017990112 0.50028109550476074 0.50004816055297852 0.4999786913394928 0.50002127885818481 -0.49995192885398865
good: 0.49978336691856384 0.49977511167526245 0.50022482872009277 -0.50021666288375854
bad : -0.30385482311248779 -0.30387380719184875 -0.30430680513381958 0.30432581901550293
DIFF!
SinTheta 0.00048828122090000000
A 0.5079689621925354
-0.49971881508827209 -0.49972546100616455 -0.50027436017990112 0.50028109550476074 0.50004816055297852 0.4999786913394928 0.50002127885818481 -0.49995192885398865
good: 0.499886155128479 0.49985414743423462 0.50014585256576538 -0.50011396408081055
bad : 0.0081317871809005737 0.008093222975730896 0.0078447908163070679 -0.007806241512298584
DIFF!
SinTheta 0.00048828122090000000
A 0.7983090877532959
-0.49971881508827209 -0.49972546100616455 -0.50027436017990112 0.50028109550476074 0.50004816055297852 0.4999786913394928 0.50002127885818481 -0.49995192885398865
good: 0.49998176097869873 0.49992763996124268 0.50007236003875732 -0.50001835823059082
bad : 0.29840424656867981 0.29834744334220886 0.29827073216438293 -0.29821401834487915
DIFF!
SinTheta 0.00069053389600000000
A 0.054238788783550262
0.50011414289474487 0.50011003017425537 0.49988996982574463 -0.49988585710525513 -0.49970793724060059 -0.49970951676368713 -0.5002903938293457 0.50029188394546509
good: -0.50009214878082275 -0.50008833408355713 -0.49991172552108765 0.49990791082382202
bad : 0.44588500261306763 0.44588103890419006 0.44564139842987061 -0.44563743472099304
DIFF!
SinTheta 0.00069053389600000000
A 0.3701384961605072
0.50011414289474487 0.50011003017425537 0.49988996982574463 -0.49988585710525513 -0.49970793724060059 -0.49970951676368713 -0.5002903938293457 0.50029188394546509
good: -0.49996381998062134 -0.49996179342269897 -0.50003820657730103 0.50003618001937866
bad : 0.13004148006439209 0.13003829121589661 0.12968471646308899 -0.12968157231807709
DIFF!
SinTheta 0.00069053389600000000
A 0.68378734588623047
0.50011414289474487 0.50011003017425537 0.49988996982574463 -0.49988585710525513 -0.49970793724060059 -0.49970951676368713 -0.5002903938293457 0.50029188394546509
good: -0.49983644485473633 -0.49983620643615723 -0.50016379356384277 0.50016355514526367
bad : -0.18355154991149902 -0.18355391919612885 -0.18402071297168732 0.18402302265167236
DIFF!
SinTheta 0.00069053389600000000
A 0.9893985390663147
0.50011414289474487 0.50011003017425537 0.49988996982574463 -0.49988585710525513 -0.49970793724060059 -0.49970951676368713 -0.5002903938293457 0.50029188394546509
good: -0.49971228837966919 -0.49971377849578857 -0.50028616189956665 0.50028759241104126
bad : -0.48910835385322571 -0.48910996317863464 -0.48968702554702759 0.48968854546546936
DIFF!
These were calculated by test code in SLerp that detects when result of 2 branches
would be different:
if (SinTheta <= 0.001) and (SinTheta > 1E-6) then
begin
W1 := NegateOneQuaternion * Sin( (1-A) * Theta ) / SinTheta;
W2 := Sin( A * Theta ) / SinTheta;
Good.Data.Vector4 := (Q1.Data.Vector4 * W1) + (Q2.Data.Vector4 * W2);
W1 := 1 - A;
W2 := A;
Bad.Data.Vector4 := (Q1.Data.Vector4 * W1) + (Q2.Data.Vector4 * W2);
if not TVector4.Equals(Bad.Data.Vector4, Good.Data.Vector4) then
begin
Writeln('SinTheta ', SinTheta:1:20);
Writeln(Format('A %g', [A]));
Writeln(Format('%s %s', [Q1.Data.Vector4.ToRawString, Q2.Data.Vector4.ToRawString]));
Writeln('good: ', Good.Data.Vector4.ToRawString);
Writeln('bad : ', Bad.Data.Vector4.ToRawString);
Writeln('DIFF!');
end;
end;
}
var
A: Single;
Q1, Q2: TQuaternion;
begin
A := 0.19590963423252106;
Q1.Data.Vector4 := Vector4(-0.49971881508827209, -0.49972546100616455, -0.50027436017990112, 0.50028109550476074);
Q2.Data.Vector4 := Vector4(0.50004816055297852, 0.4999786913394928, 0.50002127885818481, -0.49995192885398865);
AssertVectorEquals(Vector4(0.49978336691856384, 0.49977511167526245, 0.50022482872009277, -0.50021666288375854),
SLerp(A, Q1, Q2).Data.Vector4,
0.01);
A := 0.5079689621925354;
Q1.Data.Vector4 := Vector4(-0.49971881508827209, -0.49972546100616455, -0.50027436017990112, 0.50028109550476074);
Q2.Data.Vector4 := Vector4(0.50004816055297852, 0.4999786913394928, 0.50002127885818481, -0.49995192885398865);
AssertVectorEquals(Vector4(0.499886155128479, 0.49985414743423462, 0.50014585256576538, -0.50011396408081055),
SLerp(A, Q1, Q2).Data.Vector4,
0.01);
A := 0.7983090877532959;
Q1.Data.Vector4 := Vector4(-0.49971881508827209, -0.49972546100616455, -0.50027436017990112, 0.50028109550476074);
Q2.Data.Vector4 := Vector4(0.50004816055297852, 0.4999786913394928, 0.50002127885818481, -0.49995192885398865);
AssertVectorEquals(Vector4(0.49998176097869873, 0.49992763996124268, 0.50007236003875732, -0.50001835823059082),
SLerp(A, Q1, Q2).Data.Vector4,
0.01);
A := 0.054238788783550262;
Q1.Data.Vector4 := Vector4(0.50011414289474487, 0.50011003017425537, 0.49988996982574463, -0.49988585710525513);
Q2.Data.Vector4 := Vector4(-0.49970793724060059, -0.49970951676368713, -0.5002903938293457, 0.50029188394546509);
AssertVectorEquals(Vector4(-0.50009214878082275, -0.50008833408355713, -0.49991172552108765, 0.49990791082382202),
SLerp(A, Q1, Q2).Data.Vector4,
0.01);
A := 0.3701384961605072;
Q1.Data.Vector4 := Vector4(0.50011414289474487, 0.50011003017425537, 0.49988996982574463, -0.49988585710525513);
Q2.Data.Vector4 := Vector4(-0.49970793724060059, -0.49970951676368713, -0.5002903938293457, 0.50029188394546509);
AssertVectorEquals(Vector4(-0.49996381998062134, -0.49996179342269897, -0.50003820657730103, 0.50003618001937866),
SLerp(A, Q1, Q2).Data.Vector4,
0.01);
A := 0.68378734588623047;
Q1.Data.Vector4 := Vector4(0.50011414289474487, 0.50011003017425537, 0.49988996982574463, -0.49988585710525513);
Q2.Data.Vector4 := Vector4(-0.49970793724060059, -0.49970951676368713, -0.5002903938293457, 0.50029188394546509);
AssertVectorEquals(Vector4(-0.49983644485473633, -0.49983620643615723, -0.50016379356384277, 0.50016355514526367),
SLerp(A, Q1, Q2).Data.Vector4,
0.01);
A := 0.9893985390663147;
Q1.Data.Vector4 := Vector4(0.50011414289474487, 0.50011003017425537, 0.49988996982574463, -0.49988585710525513);
Q2.Data.Vector4 := Vector4(-0.49970793724060059, -0.49970951676368713, -0.5002903938293457, 0.50029188394546509);
AssertVectorEquals(Vector4(-0.49971228837966919, -0.49971377849578857, -0.50028616189956665, 0.50028759241104126),
SLerp(A, Q1, Q2).Data.Vector4,
0.01);
end;
initialization
RegisterTest(TTestCastleQuaternions);
end.
|
