458 lines
16 KiB
C++
458 lines
16 KiB
C++
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///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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//
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
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// in the documentation and/or other materials provided with the
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// distribution.
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// * Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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#include <testMatrix.h>
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#include "ImathMatrix.h"
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#include "ImathMatrixAlgo.h"
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#include "ImathVec.h"
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#include "ImathLimits.h"
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#include "ImathMath.h"
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#include "ImathInt64.h"
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#include "ImathRandom.h"
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#include <iostream>
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#include <assert.h>
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using namespace std;
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using IMATH_INTERNAL_NAMESPACE::Int64;
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//
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// This file is not currently intended to exhaustively test
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// the Imath Matrix33<T> and Matrix44<T> classes. We leave
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// that to PyImathTest.
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//
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// Instead, in this file we test only those aspects of the
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// Imath Matrix33<T> and Matrix44<T> classes that must be
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// or are more convenient to test from C++.
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//
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void
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testMatrix ()
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{
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cout << "Testing functions in ImathMatrix.h" << endl;
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union {float f; int i;} nanf;
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nanf.i = 0x7f800001; // NAN
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union {double d; Int64 i;} nand;
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nand.i = 0x7ff0000000000001ULL; // NAN
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{
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cout << "Imath::M33f shear functions" << endl;
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IMATH_INTERNAL_NAMESPACE::M33f m1, m2;
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m1.setShear (2.0f);
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assert
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(m1[0][0] == 1.0f && m1[0][1] == 0.0f && m1[0][2] == 0.0f &&
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m1[1][0] == 2.0f && m1[1][1] == 1.0f && m1[1][2] == 0.0f &&
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m1[2][0] == 0.0f && m1[2][1] == 0.0f && m1[2][2] == 1.0f);
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m2.setShear (IMATH_INTERNAL_NAMESPACE::V2f (3.0f, 4.0f));
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assert
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(m2[0][0] == 1.0f && m2[0][1] == 4.0f && m2[0][2] == 0.0f &&
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m2[1][0] == 3.0f && m2[1][1] == 1.0f && m2[1][2] == 0.0f &&
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m2[2][0] == 0.0f && m2[2][1] == 0.0f && m2[2][2] == 1.0f);
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m1.shear (IMATH_INTERNAL_NAMESPACE::V2f (5.0f, 6.0f));
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assert
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(m1[0][0] == 13.0f && m1[0][1] == 6.0f && m1[0][2] == 0.0f &&
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m1[1][0] == 7.0f && m1[1][1] == 1.0f && m1[1][2] == 0.0f &&
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m1[2][0] == 0.0f && m1[2][1] == 0.0f && m1[2][2] == 1.0f);
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m2.shear (7.0f);
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assert
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(m2[0][0] == 1.0f && m2[0][1] == 4.0f && m2[0][2] == 0.0f &&
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m2[1][0] == 10.0f && m2[1][1] == 29.0f && m2[1][2] == 0.0f &&
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m2[2][0] == 0.0f && m2[2][1] == 0.0f && m2[2][2] == 1.0f);
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cout << "M33f constructors and equality operators" << endl;
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IMATH_INTERNAL_NAMESPACE::M33f test(m2);
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assert(test == m2);
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IMATH_INTERNAL_NAMESPACE::M33f test2;
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assert(test != test2);
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IMATH_INTERNAL_NAMESPACE::M33f test3;
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test3.makeIdentity();
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assert(test2 == test3);
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}
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{
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cout << "M33d constructors and equality operators" << endl;
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IMATH_INTERNAL_NAMESPACE::M33d m2;
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m2[0][0] = 99.0f;
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m2[1][2] = 101.0f;
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IMATH_INTERNAL_NAMESPACE::M33d test(m2);
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assert(test == m2);
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IMATH_INTERNAL_NAMESPACE::M33d test2;
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assert(test != test2);
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IMATH_INTERNAL_NAMESPACE::M33d test3;
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test3.makeIdentity();
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assert(test2 == test3);
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IMATH_INTERNAL_NAMESPACE::M33f test4 (1.0f, 2.0f, 3.0f,
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4.0f, 5.0f, 6.0f,
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7.0f, 8.0f, 9.0f);
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IMATH_INTERNAL_NAMESPACE::M33d test5 = IMATH_INTERNAL_NAMESPACE::M33d (test4);
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assert (test5[0][0] == 1.0);
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assert (test5[0][1] == 2.0);
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assert (test5[0][2] == 3.0);
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assert (test5[1][0] == 4.0);
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assert (test5[1][1] == 5.0);
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assert (test5[1][2] == 6.0);
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assert (test5[2][0] == 7.0);
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assert (test5[2][1] == 8.0);
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assert (test5[2][2] == 9.0);
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}
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{
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IMATH_INTERNAL_NAMESPACE::M44f m2;
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m2[0][0] = 99.0f;
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m2[1][2] = 101.0f;
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cout << "M44f constructors and equality operators" << endl;
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IMATH_INTERNAL_NAMESPACE::M44f test(m2);
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assert(test == m2);
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IMATH_INTERNAL_NAMESPACE::M44f test2;
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assert(test != test2);
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IMATH_INTERNAL_NAMESPACE::M44f test3;
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test3.makeIdentity();
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assert(test2 == test3);
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//
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// Test non-equality when a NAN is in the same
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// place in two identical matrices
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//
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test2[0][0] = nanf.f;
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test3 = test2;
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assert(test2 != test3);
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}
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{
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IMATH_INTERNAL_NAMESPACE::M44d m2;
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m2[0][0] = 99.0f;
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m2[1][2] = 101.0f;
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cout << "M44d constructors and equality operators" << endl;
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IMATH_INTERNAL_NAMESPACE::M44d test(m2);
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assert(test == m2);
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IMATH_INTERNAL_NAMESPACE::M44d test2;
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assert(test != test2);
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IMATH_INTERNAL_NAMESPACE::M44d test3;
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test3.makeIdentity();
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assert(test2 == test3);
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//
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// Test non-equality when a NAN is in the same
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// place in two identical matrices
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//
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test2[0][0] = nand.d;
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test3 = test2;
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assert(test2 != test3);
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IMATH_INTERNAL_NAMESPACE::M44f test4 ( 1.0f, 2.0f, 3.0f, 4.0f,
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5.0f, 6.0f, 7.0f, 8.0f,
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9.0f, 10.0f, 11.0f, 12.0f,
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13.0f, 14.0f, 15.0f, 16.0f);
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IMATH_INTERNAL_NAMESPACE::M44d test5 = IMATH_INTERNAL_NAMESPACE::M44d (test4);
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assert (test5[0][0] == 1.0);
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assert (test5[0][1] == 2.0);
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assert (test5[0][2] == 3.0);
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assert (test5[0][3] == 4.0);
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assert (test5[1][0] == 5.0);
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assert (test5[1][1] == 6.0);
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assert (test5[1][2] == 7.0);
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assert (test5[1][3] == 8.0);
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assert (test5[2][0] == 9.0);
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assert (test5[2][1] == 10.0);
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assert (test5[2][2] == 11.0);
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assert (test5[2][3] == 12.0);
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assert (test5[3][0] == 13.0);
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assert (test5[3][1] == 14.0);
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assert (test5[3][2] == 15.0);
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assert (test5[3][3] == 16.0);
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}
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{
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cout << "Converting between M33 and M44" << endl;
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IMATH_INTERNAL_NAMESPACE::M44d m1;
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m1[0][0] = 99;
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IMATH_INTERNAL_NAMESPACE::M44f m2;
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m2.setValue(m1);
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assert(m2[0][0] == (float)m1[0][0]);
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m1[0][0] = 101;
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m1.setValue(m2);
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assert(m2[0][0] == (float)m1[0][0]);
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}
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// Matrix minors
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{
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cout << "3x3 Matrix minors" << endl;
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IMATH_INTERNAL_NAMESPACE::M33f a(1,2,3,4,5,6,7,8,9);
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assert (a.minorOf(0,0) == a.fastMinor(1,2,1,2));
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assert (a.minorOf(0,1) == a.fastMinor(1,2,0,2));
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assert (a.minorOf(0,2) == a.fastMinor(1,2,0,1));
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assert (a.minorOf(1,0) == a.fastMinor(0,2,1,2));
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assert (a.minorOf(1,1) == a.fastMinor(0,2,0,2));
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assert (a.minorOf(1,2) == a.fastMinor(0,2,0,1));
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assert (a.minorOf(2,0) == a.fastMinor(0,1,1,2));
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assert (a.minorOf(2,1) == a.fastMinor(0,1,0,2));
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assert (a.minorOf(2,2) == a.fastMinor(0,1,0,1));
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}
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{
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IMATH_INTERNAL_NAMESPACE::M33d a(1,2,3,4,5,6,7,8,9);
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assert (a.minorOf(0,0) == a.fastMinor(1,2,1,2));
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assert (a.minorOf(0,1) == a.fastMinor(1,2,0,2));
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assert (a.minorOf(0,2) == a.fastMinor(1,2,0,1));
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assert (a.minorOf(1,0) == a.fastMinor(0,2,1,2));
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assert (a.minorOf(1,1) == a.fastMinor(0,2,0,2));
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assert (a.minorOf(1,2) == a.fastMinor(0,2,0,1));
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assert (a.minorOf(2,0) == a.fastMinor(0,1,1,2));
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assert (a.minorOf(2,1) == a.fastMinor(0,1,0,2));
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assert (a.minorOf(2,2) == a.fastMinor(0,1,0,1));
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}
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// Determinants (by building a random singular value decomposition)
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{
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cout << "3x3 determinant" << endl;
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IMATH_INTERNAL_NAMESPACE::Rand32 random;
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IMATH_INTERNAL_NAMESPACE::M33f u;
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IMATH_INTERNAL_NAMESPACE::M33f v;
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IMATH_INTERNAL_NAMESPACE::M33f s;
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u.setRotation( random.nextf() );
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v.setRotation( random.nextf() );
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s[0][0] = random.nextf();
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s[1][1] = random.nextf();
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s[2][2] = random.nextf();
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IMATH_INTERNAL_NAMESPACE::M33f c = u * s * v.transpose();
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assert (fabsf(c.determinant() - s[0][0]*s[1][1]*s[2][2]) <= u.baseTypeEpsilon());
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}
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{
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IMATH_INTERNAL_NAMESPACE::Rand32 random;
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IMATH_INTERNAL_NAMESPACE::M33d u;
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IMATH_INTERNAL_NAMESPACE::M33d v;
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IMATH_INTERNAL_NAMESPACE::M33d s;
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u.setRotation( (double)random.nextf() );
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v.setRotation( (double)random.nextf() );
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s[0][0] = (double)random.nextf();
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s[1][1] = (double)random.nextf();
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s[2][2] = (double)random.nextf();
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IMATH_INTERNAL_NAMESPACE::M33d c = u * s * v.transpose();
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assert (fabs(c.determinant() - s[0][0]*s[1][1]*s[2][2]) <= u.baseTypeEpsilon());
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}
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// Outer product of two 3D vectors
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{
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cout << "Outer product of two 3D vectors" << endl;
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IMATH_INTERNAL_NAMESPACE::V3f a(1,2,3);
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IMATH_INTERNAL_NAMESPACE::V3f b(4,5,6);
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IMATH_INTERNAL_NAMESPACE::M33f p = IMATH_INTERNAL_NAMESPACE::outerProduct(a,b);
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for (int i=0; i<3; i++ )
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{
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for (int j=0; j<3; j++)
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{
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assert (p[i][j] == a[i]*b[j]);
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}
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}
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}
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{
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IMATH_INTERNAL_NAMESPACE::V3d a(1,2,3);
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IMATH_INTERNAL_NAMESPACE::V3d b(4,5,6);
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IMATH_INTERNAL_NAMESPACE::M33d p = IMATH_INTERNAL_NAMESPACE::outerProduct(a,b);
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|
|
|
||
|
|
for (int i=0; i<3; i++ )
|
||
|
|
{
|
||
|
|
for (int j=0; j<3; j++)
|
||
|
|
{
|
||
|
|
assert (p[i][j] == a[i]*b[j]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Determinants (by building a random singular value decomposition)
|
||
|
|
{
|
||
|
|
cout << "4x4 determinants" << endl;
|
||
|
|
|
||
|
|
IMATH_INTERNAL_NAMESPACE::Rand32 random;
|
||
|
|
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44f u = IMATH_INTERNAL_NAMESPACE::rotationMatrix
|
||
|
|
( IMATH_INTERNAL_NAMESPACE::V3f(random.nextf(),random.nextf(),random.nextf()).normalize(),
|
||
|
|
IMATH_INTERNAL_NAMESPACE::V3f(random.nextf(),random.nextf(),random.nextf()).normalize() );
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44f v = IMATH_INTERNAL_NAMESPACE::rotationMatrix
|
||
|
|
( IMATH_INTERNAL_NAMESPACE::V3f(random.nextf(),random.nextf(),random.nextf()).normalize(),
|
||
|
|
IMATH_INTERNAL_NAMESPACE::V3f(random.nextf(),random.nextf(),random.nextf()).normalize() );
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44f s;
|
||
|
|
|
||
|
|
s[0][0] = random.nextf();
|
||
|
|
s[1][1] = random.nextf();
|
||
|
|
s[2][2] = random.nextf();
|
||
|
|
s[3][3] = random.nextf();
|
||
|
|
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44f c = u * s * v.transpose();
|
||
|
|
assert (fabsf(c.determinant() - s[0][0]*s[1][1]*s[2][2]*s[3][3]) <= u.baseTypeEpsilon());
|
||
|
|
}
|
||
|
|
{
|
||
|
|
IMATH_INTERNAL_NAMESPACE::Rand32 random;
|
||
|
|
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44d u = IMATH_INTERNAL_NAMESPACE::rotationMatrix
|
||
|
|
( IMATH_INTERNAL_NAMESPACE::V3d(random.nextf(),random.nextf(),random.nextf()).normalize(),
|
||
|
|
IMATH_INTERNAL_NAMESPACE::V3d(random.nextf(),random.nextf(),random.nextf()).normalize() );
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44d v = IMATH_INTERNAL_NAMESPACE::rotationMatrix
|
||
|
|
( IMATH_INTERNAL_NAMESPACE::V3d(random.nextf(),random.nextf(),random.nextf()).normalize(),
|
||
|
|
IMATH_INTERNAL_NAMESPACE::V3d(random.nextf(),random.nextf(),random.nextf()).normalize() );
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44d s;
|
||
|
|
|
||
|
|
s[0][0] = random.nextf();
|
||
|
|
s[1][1] = random.nextf();
|
||
|
|
s[2][2] = random.nextf();
|
||
|
|
s[3][3] = random.nextf();
|
||
|
|
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44d c = u * s * v.transpose();
|
||
|
|
assert (fabs(c.determinant() - s[0][0]*s[1][1]*s[2][2]*s[3][3]) <= u.baseTypeEpsilon());
|
||
|
|
}
|
||
|
|
|
||
|
|
// Matrix minors
|
||
|
|
{
|
||
|
|
cout << "4x4 matrix minors" << endl;
|
||
|
|
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44d a(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);
|
||
|
|
|
||
|
|
assert (a.minorOf(0,0) == a.fastMinor(1,2,3,1,2,3));
|
||
|
|
assert (a.minorOf(0,1) == a.fastMinor(1,2,3,0,2,3));
|
||
|
|
assert (a.minorOf(0,2) == a.fastMinor(1,2,3,0,1,3));
|
||
|
|
assert (a.minorOf(0,3) == a.fastMinor(1,2,3,0,1,2));
|
||
|
|
assert (a.minorOf(1,0) == a.fastMinor(0,2,3,1,2,3));
|
||
|
|
assert (a.minorOf(1,1) == a.fastMinor(0,2,3,0,2,3));
|
||
|
|
assert (a.minorOf(1,2) == a.fastMinor(0,2,3,0,1,3));
|
||
|
|
assert (a.minorOf(1,3) == a.fastMinor(0,2,3,0,1,2));
|
||
|
|
assert (a.minorOf(2,0) == a.fastMinor(0,1,3,1,2,3));
|
||
|
|
assert (a.minorOf(2,1) == a.fastMinor(0,1,3,0,2,3));
|
||
|
|
assert (a.minorOf(2,2) == a.fastMinor(0,1,3,0,1,3));
|
||
|
|
assert (a.minorOf(2,3) == a.fastMinor(0,1,3,0,1,2));
|
||
|
|
assert (a.minorOf(3,0) == a.fastMinor(0,1,2,1,2,3));
|
||
|
|
assert (a.minorOf(3,1) == a.fastMinor(0,1,2,0,2,3));
|
||
|
|
assert (a.minorOf(3,2) == a.fastMinor(0,1,2,0,1,3));
|
||
|
|
assert (a.minorOf(3,3) == a.fastMinor(0,1,2,0,1,2));
|
||
|
|
}
|
||
|
|
{
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44f a(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);
|
||
|
|
|
||
|
|
assert (a.minorOf(0,0) == a.fastMinor(1,2,3,1,2,3));
|
||
|
|
assert (a.minorOf(0,1) == a.fastMinor(1,2,3,0,2,3));
|
||
|
|
assert (a.minorOf(0,2) == a.fastMinor(1,2,3,0,1,3));
|
||
|
|
assert (a.minorOf(0,3) == a.fastMinor(1,2,3,0,1,2));
|
||
|
|
assert (a.minorOf(1,0) == a.fastMinor(0,2,3,1,2,3));
|
||
|
|
assert (a.minorOf(1,1) == a.fastMinor(0,2,3,0,2,3));
|
||
|
|
assert (a.minorOf(1,2) == a.fastMinor(0,2,3,0,1,3));
|
||
|
|
assert (a.minorOf(1,3) == a.fastMinor(0,2,3,0,1,2));
|
||
|
|
assert (a.minorOf(2,0) == a.fastMinor(0,1,3,1,2,3));
|
||
|
|
assert (a.minorOf(2,1) == a.fastMinor(0,1,3,0,2,3));
|
||
|
|
assert (a.minorOf(2,2) == a.fastMinor(0,1,3,0,1,3));
|
||
|
|
assert (a.minorOf(2,3) == a.fastMinor(0,1,3,0,1,2));
|
||
|
|
assert (a.minorOf(3,0) == a.fastMinor(0,1,2,1,2,3));
|
||
|
|
assert (a.minorOf(3,1) == a.fastMinor(0,1,2,0,2,3));
|
||
|
|
assert (a.minorOf(3,2) == a.fastMinor(0,1,2,0,1,3));
|
||
|
|
assert (a.minorOf(3,3) == a.fastMinor(0,1,2,0,1,2));
|
||
|
|
}
|
||
|
|
|
||
|
|
// VC 2005 64 bits compiler has a bug with __restrict keword.
|
||
|
|
// Pointers with __restrict should not alias the same symbol.
|
||
|
|
// But, with optimization on, VC removes intermediate temp variable
|
||
|
|
// and ignores __restrict.
|
||
|
|
{
|
||
|
|
cout << "M44 multiplicaftion test" << endl;
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44f M ( 1.0f, 2.0f, 3.0f, 4.0f,
|
||
|
|
5.0f, 6.0f, 7.0f, 8.0f,
|
||
|
|
9.0f, 10.0f, 11.0f, 12.0f,
|
||
|
|
13.0f, 14.0f, 15.0f, 16.0f);
|
||
|
|
|
||
|
|
IMATH_INTERNAL_NAMESPACE::M44f N; N.makeIdentity();
|
||
|
|
|
||
|
|
// N should be equal to M
|
||
|
|
// This typical test fails
|
||
|
|
// when __restrict is used for pointers in "multiply" function.
|
||
|
|
N = N * M;
|
||
|
|
|
||
|
|
assert(N == M);
|
||
|
|
|
||
|
|
if (N != M) {
|
||
|
|
cout << "M44 multiplication test has failed, error." << endl
|
||
|
|
<< "M" << endl << M << endl
|
||
|
|
<< "N" << endl << N << endl;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
cout << "ok\n" << endl;
|
||
|
|
}
|