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@@ -8,56 +8,56 @@
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namespace bs
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{
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- const Matrix4 Matrix4::ZERO(
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- 0.0f, 0.0f, 0.0f, 0.0f,
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- 0.0f, 0.0f, 0.0f, 0.0f,
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- 0.0f, 0.0f, 0.0f, 0.0f,
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- 0.0f, 0.0f, 0.0f, 0.0f);
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+ const Matrix4 Matrix4::ZERO(
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+ 0.0f, 0.0f, 0.0f, 0.0f,
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+ 0.0f, 0.0f, 0.0f, 0.0f,
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+ 0.0f, 0.0f, 0.0f, 0.0f,
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+ 0.0f, 0.0f, 0.0f, 0.0f);
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- const Matrix4 Matrix4::IDENTITY(
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+ const Matrix4 Matrix4::IDENTITY(
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1.0f, 0.0f, 0.0f, 0.0f,
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0.0f, 1.0f, 0.0f, 0.0f,
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0.0f, 0.0f, 1.0f, 0.0f,
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0.0f, 0.0f, 0.0f, 1.0f);
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- static float MINOR(const Matrix4& m, const UINT32 r0, const UINT32 r1, const UINT32 r2,
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+ static float MINOR(const Matrix4& m, const UINT32 r0, const UINT32 r1, const UINT32 r2,
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const UINT32 c0, const UINT32 c1, const UINT32 c2)
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- {
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- return m[r0][c0] * (m[r1][c1] * m[r2][c2] - m[r2][c1] * m[r1][c2]) -
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- m[r0][c1] * (m[r1][c0] * m[r2][c2] - m[r2][c0] * m[r1][c2]) +
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- m[r0][c2] * (m[r1][c0] * m[r2][c1] - m[r2][c0] * m[r1][c1]);
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- }
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-
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- Matrix4 Matrix4::adjoint() const
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- {
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- return Matrix4( MINOR(*this, 1, 2, 3, 1, 2, 3),
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- -MINOR(*this, 0, 2, 3, 1, 2, 3),
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- MINOR(*this, 0, 1, 3, 1, 2, 3),
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- -MINOR(*this, 0, 1, 2, 1, 2, 3),
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-
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- -MINOR(*this, 1, 2, 3, 0, 2, 3),
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- MINOR(*this, 0, 2, 3, 0, 2, 3),
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- -MINOR(*this, 0, 1, 3, 0, 2, 3),
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- MINOR(*this, 0, 1, 2, 0, 2, 3),
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-
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- MINOR(*this, 1, 2, 3, 0, 1, 3),
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- -MINOR(*this, 0, 2, 3, 0, 1, 3),
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- MINOR(*this, 0, 1, 3, 0, 1, 3),
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- -MINOR(*this, 0, 1, 2, 0, 1, 3),
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-
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- -MINOR(*this, 1, 2, 3, 0, 1, 2),
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- MINOR(*this, 0, 2, 3, 0, 1, 2),
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- -MINOR(*this, 0, 1, 3, 0, 1, 2),
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- MINOR(*this, 0, 1, 2, 0, 1, 2));
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- }
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-
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- float Matrix4::determinant() const
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- {
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- return m[0][0] * MINOR(*this, 1, 2, 3, 1, 2, 3) -
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- m[0][1] * MINOR(*this, 1, 2, 3, 0, 2, 3) +
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- m[0][2] * MINOR(*this, 1, 2, 3, 0, 1, 3) -
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- m[0][3] * MINOR(*this, 1, 2, 3, 0, 1, 2);
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- }
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+ {
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+ return m[r0][c0] * (m[r1][c1] * m[r2][c2] - m[r2][c1] * m[r1][c2]) -
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+ m[r0][c1] * (m[r1][c0] * m[r2][c2] - m[r2][c0] * m[r1][c2]) +
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+ m[r0][c2] * (m[r1][c0] * m[r2][c1] - m[r2][c0] * m[r1][c1]);
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+ }
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+
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+ Matrix4 Matrix4::adjoint() const
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+ {
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+ return Matrix4( MINOR(*this, 1, 2, 3, 1, 2, 3),
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+ -MINOR(*this, 0, 2, 3, 1, 2, 3),
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+ MINOR(*this, 0, 1, 3, 1, 2, 3),
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+ -MINOR(*this, 0, 1, 2, 1, 2, 3),
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+
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+ -MINOR(*this, 1, 2, 3, 0, 2, 3),
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+ MINOR(*this, 0, 2, 3, 0, 2, 3),
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+ -MINOR(*this, 0, 1, 3, 0, 2, 3),
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+ MINOR(*this, 0, 1, 2, 0, 2, 3),
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+
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+ MINOR(*this, 1, 2, 3, 0, 1, 3),
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+ -MINOR(*this, 0, 2, 3, 0, 1, 3),
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+ MINOR(*this, 0, 1, 3, 0, 1, 3),
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+ -MINOR(*this, 0, 1, 2, 0, 1, 3),
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+
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+ -MINOR(*this, 1, 2, 3, 0, 1, 2),
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+ MINOR(*this, 0, 2, 3, 0, 1, 2),
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+ -MINOR(*this, 0, 1, 3, 0, 1, 2),
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+ MINOR(*this, 0, 1, 2, 0, 1, 2));
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+ }
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+
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+ float Matrix4::determinant() const
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+ {
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+ return m[0][0] * MINOR(*this, 1, 2, 3, 1, 2, 3) -
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+ m[0][1] * MINOR(*this, 1, 2, 3, 0, 2, 3) +
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+ m[0][2] * MINOR(*this, 1, 2, 3, 0, 1, 3) -
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+ m[0][3] * MINOR(*this, 1, 2, 3, 0, 1, 2);
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+ }
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float Matrix4::determinant3x3() const
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{
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@@ -70,149 +70,149 @@ namespace bs
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return det;
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}
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- Matrix4 Matrix4::inverse() const
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- {
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- float m00 = m[0][0], m01 = m[0][1], m02 = m[0][2], m03 = m[0][3];
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- float m10 = m[1][0], m11 = m[1][1], m12 = m[1][2], m13 = m[1][3];
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- float m20 = m[2][0], m21 = m[2][1], m22 = m[2][2], m23 = m[2][3];
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- float m30 = m[3][0], m31 = m[3][1], m32 = m[3][2], m33 = m[3][3];
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-
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- float v0 = m20 * m31 - m21 * m30;
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- float v1 = m20 * m32 - m22 * m30;
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- float v2 = m20 * m33 - m23 * m30;
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- float v3 = m21 * m32 - m22 * m31;
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- float v4 = m21 * m33 - m23 * m31;
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- float v5 = m22 * m33 - m23 * m32;
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-
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- float t00 = + (v5 * m11 - v4 * m12 + v3 * m13);
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- float t10 = - (v5 * m10 - v2 * m12 + v1 * m13);
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- float t20 = + (v4 * m10 - v2 * m11 + v0 * m13);
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- float t30 = - (v3 * m10 - v1 * m11 + v0 * m12);
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-
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- float invDet = 1 / (t00 * m00 + t10 * m01 + t20 * m02 + t30 * m03);
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-
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- float d00 = t00 * invDet;
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- float d10 = t10 * invDet;
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- float d20 = t20 * invDet;
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- float d30 = t30 * invDet;
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-
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- float d01 = - (v5 * m01 - v4 * m02 + v3 * m03) * invDet;
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- float d11 = + (v5 * m00 - v2 * m02 + v1 * m03) * invDet;
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- float d21 = - (v4 * m00 - v2 * m01 + v0 * m03) * invDet;
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- float d31 = + (v3 * m00 - v1 * m01 + v0 * m02) * invDet;
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-
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- v0 = m10 * m31 - m11 * m30;
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- v1 = m10 * m32 - m12 * m30;
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- v2 = m10 * m33 - m13 * m30;
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- v3 = m11 * m32 - m12 * m31;
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- v4 = m11 * m33 - m13 * m31;
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- v5 = m12 * m33 - m13 * m32;
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-
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- float d02 = + (v5 * m01 - v4 * m02 + v3 * m03) * invDet;
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- float d12 = - (v5 * m00 - v2 * m02 + v1 * m03) * invDet;
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- float d22 = + (v4 * m00 - v2 * m01 + v0 * m03) * invDet;
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- float d32 = - (v3 * m00 - v1 * m01 + v0 * m02) * invDet;
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-
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- v0 = m21 * m10 - m20 * m11;
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- v1 = m22 * m10 - m20 * m12;
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- v2 = m23 * m10 - m20 * m13;
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- v3 = m22 * m11 - m21 * m12;
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- v4 = m23 * m11 - m21 * m13;
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- v5 = m23 * m12 - m22 * m13;
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-
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- float d03 = - (v5 * m01 - v4 * m02 + v3 * m03) * invDet;
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- float d13 = + (v5 * m00 - v2 * m02 + v1 * m03) * invDet;
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- float d23 = - (v4 * m00 - v2 * m01 + v0 * m03) * invDet;
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- float d33 = + (v3 * m00 - v1 * m01 + v0 * m02) * invDet;
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+ Matrix4 Matrix4::inverse() const
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+ {
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+ float m00 = m[0][0], m01 = m[0][1], m02 = m[0][2], m03 = m[0][3];
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+ float m10 = m[1][0], m11 = m[1][1], m12 = m[1][2], m13 = m[1][3];
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+ float m20 = m[2][0], m21 = m[2][1], m22 = m[2][2], m23 = m[2][3];
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+ float m30 = m[3][0], m31 = m[3][1], m32 = m[3][2], m33 = m[3][3];
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+
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+ float v0 = m20 * m31 - m21 * m30;
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+ float v1 = m20 * m32 - m22 * m30;
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+ float v2 = m20 * m33 - m23 * m30;
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+ float v3 = m21 * m32 - m22 * m31;
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+ float v4 = m21 * m33 - m23 * m31;
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+ float v5 = m22 * m33 - m23 * m32;
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+
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+ float t00 = + (v5 * m11 - v4 * m12 + v3 * m13);
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+ float t10 = - (v5 * m10 - v2 * m12 + v1 * m13);
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+ float t20 = + (v4 * m10 - v2 * m11 + v0 * m13);
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+ float t30 = - (v3 * m10 - v1 * m11 + v0 * m12);
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+
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+ float invDet = 1 / (t00 * m00 + t10 * m01 + t20 * m02 + t30 * m03);
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+
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+ float d00 = t00 * invDet;
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+ float d10 = t10 * invDet;
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+ float d20 = t20 * invDet;
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+ float d30 = t30 * invDet;
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+
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+ float d01 = - (v5 * m01 - v4 * m02 + v3 * m03) * invDet;
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+ float d11 = + (v5 * m00 - v2 * m02 + v1 * m03) * invDet;
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+ float d21 = - (v4 * m00 - v2 * m01 + v0 * m03) * invDet;
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+ float d31 = + (v3 * m00 - v1 * m01 + v0 * m02) * invDet;
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+
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+ v0 = m10 * m31 - m11 * m30;
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+ v1 = m10 * m32 - m12 * m30;
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+ v2 = m10 * m33 - m13 * m30;
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+ v3 = m11 * m32 - m12 * m31;
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+ v4 = m11 * m33 - m13 * m31;
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+ v5 = m12 * m33 - m13 * m32;
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+
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+ float d02 = + (v5 * m01 - v4 * m02 + v3 * m03) * invDet;
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+ float d12 = - (v5 * m00 - v2 * m02 + v1 * m03) * invDet;
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+ float d22 = + (v4 * m00 - v2 * m01 + v0 * m03) * invDet;
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+ float d32 = - (v3 * m00 - v1 * m01 + v0 * m02) * invDet;
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+
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+ v0 = m21 * m10 - m20 * m11;
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+ v1 = m22 * m10 - m20 * m12;
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+ v2 = m23 * m10 - m20 * m13;
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+ v3 = m22 * m11 - m21 * m12;
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+ v4 = m23 * m11 - m21 * m13;
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+ v5 = m23 * m12 - m22 * m13;
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+
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+ float d03 = - (v5 * m01 - v4 * m02 + v3 * m03) * invDet;
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+ float d13 = + (v5 * m00 - v2 * m02 + v1 * m03) * invDet;
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+ float d23 = - (v4 * m00 - v2 * m01 + v0 * m03) * invDet;
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+ float d33 = + (v3 * m00 - v1 * m01 + v0 * m02) * invDet;
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- return Matrix4(
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- d00, d01, d02, d03,
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- d10, d11, d12, d13,
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- d20, d21, d22, d23,
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- d30, d31, d32, d33);
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- }
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-
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- Matrix4 Matrix4::inverseAffine() const
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- {
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- BS_ASSERT(isAffine());
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-
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- float m10 = m[1][0], m11 = m[1][1], m12 = m[1][2];
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- float m20 = m[2][0], m21 = m[2][1], m22 = m[2][2];
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-
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- float t00 = m22 * m11 - m21 * m12;
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- float t10 = m20 * m12 - m22 * m10;
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- float t20 = m21 * m10 - m20 * m11;
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-
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- float m00 = m[0][0], m01 = m[0][1], m02 = m[0][2];
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-
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- float invDet = 1 / (m00 * t00 + m01 * t10 + m02 * t20);
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-
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- t00 *= invDet; t10 *= invDet; t20 *= invDet;
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-
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- m00 *= invDet; m01 *= invDet; m02 *= invDet;
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-
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- float r00 = t00;
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- float r01 = m02 * m21 - m01 * m22;
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- float r02 = m01 * m12 - m02 * m11;
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-
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- float r10 = t10;
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- float r11 = m00 * m22 - m02 * m20;
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- float r12 = m02 * m10 - m00 * m12;
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-
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- float r20 = t20;
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- float r21 = m01 * m20 - m00 * m21;
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- float r22 = m00 * m11 - m01 * m10;
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-
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- float m03 = m[0][3], m13 = m[1][3], m23 = m[2][3];
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-
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- float r03 = - (r00 * m03 + r01 * m13 + r02 * m23);
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- float r13 = - (r10 * m03 + r11 * m13 + r12 * m23);
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- float r23 = - (r20 * m03 + r21 * m13 + r22 * m23);
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-
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- return Matrix4(
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- r00, r01, r02, r03,
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- r10, r11, r12, r13,
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- r20, r21, r22, r23,
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- 0, 0, 0, 1);
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- }
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-
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- void Matrix4::setTRS(const Vector3& translation, const Quaternion& rotation, const Vector3& scale)
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- {
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- Matrix3 rot3x3;
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- rotation.toRotationMatrix(rot3x3);
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-
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- m[0][0] = scale.x * rot3x3[0][0]; m[0][1] = scale.y * rot3x3[0][1]; m[0][2] = scale.z * rot3x3[0][2]; m[0][3] = translation.x;
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- m[1][0] = scale.x * rot3x3[1][0]; m[1][1] = scale.y * rot3x3[1][1]; m[1][2] = scale.z * rot3x3[1][2]; m[1][3] = translation.y;
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- m[2][0] = scale.x * rot3x3[2][0]; m[2][1] = scale.y * rot3x3[2][1]; m[2][2] = scale.z * rot3x3[2][2]; m[2][3] = translation.z;
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-
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- // No projection term
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- m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1;
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- }
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-
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- void Matrix4::setInverseTRS(const Vector3& translation, const Quaternion& rotation, const Vector3& scale)
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- {
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- // Invert the parameters
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- Vector3 invTranslate = -translation;
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- Vector3 invScale(1 / scale.x, 1 / scale.y, 1 / scale.z);
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- Quaternion invRot = rotation.inverse();
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-
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- // Because we're inverting, order is translation, rotation, scale
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- // So make translation relative to scale & rotation
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- invTranslate = invRot.rotate(invTranslate);
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- invTranslate *= invScale;
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-
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- // Next, make a 3x3 rotation matrix
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- Matrix3 rot3x3;
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- invRot.toRotationMatrix(rot3x3);
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-
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- // Set up final matrix with scale, rotation and translation
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- m[0][0] = invScale.x * rot3x3[0][0]; m[0][1] = invScale.x * rot3x3[0][1]; m[0][2] = invScale.x * rot3x3[0][2]; m[0][3] = invTranslate.x;
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- m[1][0] = invScale.y * rot3x3[1][0]; m[1][1] = invScale.y * rot3x3[1][1]; m[1][2] = invScale.y * rot3x3[1][2]; m[1][3] = invTranslate.y;
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- m[2][0] = invScale.z * rot3x3[2][0]; m[2][1] = invScale.z * rot3x3[2][1]; m[2][2] = invScale.z * rot3x3[2][2]; m[2][3] = invTranslate.z;
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-
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- // No projection term
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- m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1;
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- }
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+ return Matrix4(
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+ d00, d01, d02, d03,
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+ d10, d11, d12, d13,
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+ d20, d21, d22, d23,
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+ d30, d31, d32, d33);
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|
+ }
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+
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+ Matrix4 Matrix4::inverseAffine() const
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+ {
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|
+ BS_ASSERT(isAffine());
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+
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|
+ float m10 = m[1][0], m11 = m[1][1], m12 = m[1][2];
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|
+ float m20 = m[2][0], m21 = m[2][1], m22 = m[2][2];
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+
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+ float t00 = m22 * m11 - m21 * m12;
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|
+ float t10 = m20 * m12 - m22 * m10;
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|
+ float t20 = m21 * m10 - m20 * m11;
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|
+
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|
+ float m00 = m[0][0], m01 = m[0][1], m02 = m[0][2];
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|
+
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|
+ float invDet = 1 / (m00 * t00 + m01 * t10 + m02 * t20);
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|
+
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|
|
+ t00 *= invDet; t10 *= invDet; t20 *= invDet;
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|
+
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|
|
+ m00 *= invDet; m01 *= invDet; m02 *= invDet;
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|
+
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|
|
+ float r00 = t00;
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|
|
+ float r01 = m02 * m21 - m01 * m22;
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|
|
+ float r02 = m01 * m12 - m02 * m11;
|
|
|
+
|
|
|
+ float r10 = t10;
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|
|
+ float r11 = m00 * m22 - m02 * m20;
|
|
|
+ float r12 = m02 * m10 - m00 * m12;
|
|
|
+
|
|
|
+ float r20 = t20;
|
|
|
+ float r21 = m01 * m20 - m00 * m21;
|
|
|
+ float r22 = m00 * m11 - m01 * m10;
|
|
|
+
|
|
|
+ float m03 = m[0][3], m13 = m[1][3], m23 = m[2][3];
|
|
|
+
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|
|
+ float r03 = - (r00 * m03 + r01 * m13 + r02 * m23);
|
|
|
+ float r13 = - (r10 * m03 + r11 * m13 + r12 * m23);
|
|
|
+ float r23 = - (r20 * m03 + r21 * m13 + r22 * m23);
|
|
|
+
|
|
|
+ return Matrix4(
|
|
|
+ r00, r01, r02, r03,
|
|
|
+ r10, r11, r12, r13,
|
|
|
+ r20, r21, r22, r23,
|
|
|
+ 0, 0, 0, 1);
|
|
|
+ }
|
|
|
+
|
|
|
+ void Matrix4::setTRS(const Vector3& translation, const Quaternion& rotation, const Vector3& scale)
|
|
|
+ {
|
|
|
+ Matrix3 rot3x3;
|
|
|
+ rotation.toRotationMatrix(rot3x3);
|
|
|
+
|
|
|
+ m[0][0] = scale.x * rot3x3[0][0]; m[0][1] = scale.y * rot3x3[0][1]; m[0][2] = scale.z * rot3x3[0][2]; m[0][3] = translation.x;
|
|
|
+ m[1][0] = scale.x * rot3x3[1][0]; m[1][1] = scale.y * rot3x3[1][1]; m[1][2] = scale.z * rot3x3[1][2]; m[1][3] = translation.y;
|
|
|
+ m[2][0] = scale.x * rot3x3[2][0]; m[2][1] = scale.y * rot3x3[2][1]; m[2][2] = scale.z * rot3x3[2][2]; m[2][3] = translation.z;
|
|
|
+
|
|
|
+ // No projection term
|
|
|
+ m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1;
|
|
|
+ }
|
|
|
+
|
|
|
+ void Matrix4::setInverseTRS(const Vector3& translation, const Quaternion& rotation, const Vector3& scale)
|
|
|
+ {
|
|
|
+ // Invert the parameters
|
|
|
+ Vector3 invTranslate = -translation;
|
|
|
+ Vector3 invScale(1 / scale.x, 1 / scale.y, 1 / scale.z);
|
|
|
+ Quaternion invRot = rotation.inverse();
|
|
|
+
|
|
|
+ // Because we're inverting, order is translation, rotation, scale
|
|
|
+ // So make translation relative to scale & rotation
|
|
|
+ invTranslate = invRot.rotate(invTranslate);
|
|
|
+ invTranslate *= invScale;
|
|
|
+
|
|
|
+ // Next, make a 3x3 rotation matrix
|
|
|
+ Matrix3 rot3x3;
|
|
|
+ invRot.toRotationMatrix(rot3x3);
|
|
|
+
|
|
|
+ // Set up final matrix with scale, rotation and translation
|
|
|
+ m[0][0] = invScale.x * rot3x3[0][0]; m[0][1] = invScale.x * rot3x3[0][1]; m[0][2] = invScale.x * rot3x3[0][2]; m[0][3] = invTranslate.x;
|
|
|
+ m[1][0] = invScale.y * rot3x3[1][0]; m[1][1] = invScale.y * rot3x3[1][1]; m[1][2] = invScale.y * rot3x3[1][2]; m[1][3] = invTranslate.y;
|
|
|
+ m[2][0] = invScale.z * rot3x3[2][0]; m[2][1] = invScale.z * rot3x3[2][1]; m[2][2] = invScale.z * rot3x3[2][2]; m[2][3] = invTranslate.z;
|
|
|
+
|
|
|
+ // No projection term
|
|
|
+ m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1;
|
|
|
+ }
|
|
|
|
|
|
void Matrix4::decomposition(Vector3& position, Quaternion& rotation, Vector3& scale) const
|
|
|
{
|