const Matrix2x2 slerp(const Matrix2x2& a, const Matrix2x2& b, const float t) { const Matrix2x2 c = timesTranspose(a, b); const float angle = rotationAngle(c); return a * Matrix2x2::rotation(t * angle); }
const Transform2 transformByInverse(const Transform2& a, const Transform2& b) { GEOMETRY_RUNTIME_ASSERT(a.scaling > 0.0f); GEOMETRY_RUNTIME_ASSERT(b.scaling > 0.0f); return Transform2( transformByInverse(a.translation, b), timesTranspose(a.rotation, b.rotation), a.scaling / b.scaling ); }
const Vector2 transformByInverse(const Vector2& q, const Transform2& t) { GEOMETRY_RUNTIME_ASSERT(t.scaling > 0.0f); return timesTranspose(q - t.translation, t.rotation) / t.scaling; }
int Test_3x3timesTranspose(void) { // Init an array flanked by guard pages btMatrix3x3 in1[ARRAY_SIZE]; btMatrix3x3 in2[ARRAY_SIZE]; btMatrix3x3 out[ARRAY_SIZE]; btMatrix3x3 out2[ARRAY_SIZE]; // Init the data size_t i, j; for( i = 0; i < ARRAY_SIZE; i++ ) { in1[i] = btMatrix3x3(rand_f4(), rand_f4(), rand_f4() ); in2[i] = btMatrix3x3(rand_f4(), rand_f4(), rand_f4() ); out[i] = timesTranspose(in1[i], in2[i]); out2[i] = in1[i].timesTranspose(in2[i]); if( out[i] != out2[i] ) { printf( "failure @ %ld\n", i); return -1; } } uint64_t scalarTime, vectorTime; uint64_t startTime, bestTime, currentTime; bestTime = -1LL; scalarTime = 0; for (j = 0; j < LOOPCOUNT; j++) { startTime = ReadTicks(); for( i = 0; i < ARRAY_SIZE; i++ ) out[i] = timesTranspose(in1[i], in2[i]); currentTime = ReadTicks() - startTime; scalarTime += currentTime; if( currentTime < bestTime ) bestTime = currentTime; } if( 0 == gReportAverageTimes ) scalarTime = bestTime; else scalarTime /= LOOPCOUNT; bestTime = -1LL; vectorTime = 0; for (j = 0; j < LOOPCOUNT; j++) { startTime = ReadTicks(); for( i = 0; i < ARRAY_SIZE; i++ ) out[i] = in1[i].timesTranspose(in2[i]); currentTime = ReadTicks() - startTime; vectorTime += currentTime; if( currentTime < bestTime ) bestTime = currentTime; } if( 0 == gReportAverageTimes ) vectorTime = bestTime; else vectorTime /= LOOPCOUNT; vlog( "Timing:\n" ); vlog( "\t scalar\t vector\n" ); vlog( "\t%10.2f\t%10.2f\n", TicksToCycles( scalarTime ) / ARRAY_SIZE, TicksToCycles( vectorTime ) / ARRAY_SIZE ); return 0; }