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68c60f58c0
* math: fix adjoint of Matrix2 Fix the adjoint of the Matrix2x2 implementation in the math module. This also fixes the calculation of the inverse which depends on the adjoint. * update release notes
451 lines
13 KiB
Plaintext
451 lines
13 KiB
Plaintext
module std::math::matrix(<Real>);
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import std::math::vector;
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struct Matrix2x2
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{
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union
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{
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struct
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{
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Real m00, m01;
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Real m10, m11;
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}
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Real[4] m;
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}
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}
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struct Matrix3x3
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{
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union
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{
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struct
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{
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Real m00, m01, m02;
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Real m10, m11, m12;
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Real m20, m21, m22;
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}
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Real[9] m;
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}
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}
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struct Matrix4x4
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{
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union
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{
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struct
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{
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Real m00, m01, m02, m03;
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Real m10, m11, m12, m13;
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Real m20, m21, m22, m23;
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Real m30, m31, m32, m33;
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}
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Real[16] m;
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}
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}
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fn Real[<2>] Matrix2x2.apply(&self, Real[<2>] vec)
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{
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return {
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self.m00 * vec[0] + self.m01 * vec[1],
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self.m10 * vec[0] + self.m11 * vec[1],
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};
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}
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fn Real[<3>] Matrix3x3.apply(&self, Real[<3>] vec)
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{
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return {
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self.m00 * vec[0] + self.m01 * vec[1] + self.m02 * vec[2],
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self.m10 * vec[0] + self.m11 * vec[1] + self.m12 * vec[2],
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self.m20 * vec[0] + self.m21 * vec[1] + self.m22 * vec[2],
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};
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}
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fn Real[<4>] Matrix4x4.apply(&self, Real[<4>] vec)
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{
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return {
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self.m00 * vec[0] + self.m01 * vec[1] + self.m02 * vec[2] + self.m03 * vec[3],
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self.m10 * vec[0] + self.m11 * vec[1] + self.m12 * vec[2] + self.m13 * vec[3],
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self.m20 * vec[0] + self.m21 * vec[1] + self.m22 * vec[2] + self.m23 * vec[3],
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self.m30 * vec[0] + self.m31 * vec[1] + self.m32 * vec[2] + self.m33 * vec[3],
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};
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}
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fn Matrix2x2 Matrix2x2.mul(&self, Matrix2x2 b)
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{
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return {
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self.m00 * b.m00 + self.m01 * b.m10, self.m00 * b.m01 + self.m01 * b.m11,
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self.m10 * b.m00 + self.m11 * b.m10, self.m10 * b.m01 + self.m11 * b.m11,
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};
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}
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fn Matrix3x3 Matrix3x3.mul(&self, Matrix3x3 b)
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{
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return {
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self.m00 * b.m00 + self.m01 * b.m10 + self.m02 * b.m20,
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self.m00 * b.m01 + self.m01 * b.m11 + self.m02 * b.m21,
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self.m00 * b.m02 + self.m01 * b.m12 + self.m02 * b.m22,
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self.m10 * b.m00 + self.m11 * b.m10 + self.m12 * b.m20,
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self.m10 * b.m01 + self.m11 * b.m11 + self.m12 * b.m21,
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self.m10 * b.m02 + self.m11 * b.m12 + self.m12 * b.m22,
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self.m20 * b.m00 + self.m21 * b.m10 + self.m22 * b.m20,
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self.m20 * b.m01 + self.m21 * b.m11 + self.m22 * b.m21,
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self.m20 * b.m02 + self.m21 * b.m12 + self.m22 * b.m22,
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};
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}
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fn Matrix4x4 Matrix4x4.mul(Matrix4x4* a, Matrix4x4 b)
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{
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return {
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a.m00 * b.m00 + a.m01 * b.m10 + a.m02 * b.m20 + a.m03 * b.m30,
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a.m00 * b.m01 + a.m01 * b.m11 + a.m02 * b.m21 + a.m03 * b.m31,
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a.m00 * b.m02 + a.m01 * b.m12 + a.m02 * b.m22 + a.m03 * b.m32,
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a.m00 * b.m03 + a.m01 * b.m13 + a.m02 * b.m23 + a.m03 * b.m33,
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a.m10 * b.m00 + a.m11 * b.m10 + a.m12 * b.m20 + a.m13 * b.m30,
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a.m10 * b.m01 + a.m11 * b.m11 + a.m12 * b.m21 + a.m13 * b.m31,
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a.m10 * b.m02 + a.m11 * b.m12 + a.m12 * b.m22 + a.m13 * b.m32,
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a.m10 * b.m03 + a.m11 * b.m13 + a.m12 * b.m23 + a.m13 * b.m33,
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a.m20 * b.m00 + a.m21 * b.m10 + a.m22 * b.m20 + a.m23 * b.m30,
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a.m20 * b.m01 + a.m21 * b.m11 + a.m22 * b.m21 + a.m23 * b.m31,
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a.m20 * b.m02 + a.m21 * b.m12 + a.m22 * b.m22 + a.m23 * b.m32,
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a.m20 * b.m03 + a.m21 * b.m13 + a.m22 * b.m23 + a.m23 * b.m33,
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a.m30 * b.m00 + a.m31 * b.m10 + a.m32 * b.m20 + a.m33 * b.m30,
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a.m30 * b.m01 + a.m31 * b.m11 + a.m32 * b.m21 + a.m33 * b.m31,
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a.m30 * b.m02 + a.m31 * b.m12 + a.m32 * b.m22 + a.m33 * b.m32,
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a.m30 * b.m03 + a.m31 * b.m13 + a.m32 * b.m23 + a.m33 * b.m33,
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};
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}
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fn Matrix2x2 Matrix2x2.component_mul(&self, Real s) => matrix_component_mul(self, s);
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fn Matrix3x3 Matrix3x3.component_mul(&self, Real s) => matrix_component_mul(self, s);
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fn Matrix4x4 Matrix4x4.component_mul(&self, Real s) => matrix_component_mul(self, s);
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fn Matrix2x2 Matrix2x2.add(&self, Matrix2x2 mat2) => matrix_add(self, mat2);
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fn Matrix3x3 Matrix3x3.add(&self, Matrix3x3 mat2) => matrix_add(self, mat2);
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fn Matrix4x4 Matrix4x4.add(&self, Matrix4x4 mat2) => matrix_add(self, mat2);
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fn Matrix2x2 Matrix2x2.sub(&self, Matrix2x2 mat2) => matrix_sub(self, mat2);
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fn Matrix3x3 Matrix3x3.sub(&self, Matrix3x3 mat2) => matrix_sub(self, mat2);
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fn Matrix4x4 Matrix4x4.sub(&self, Matrix4x4 mat2) => matrix_sub(self, mat2);
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fn Matrix4x4 look_at(Real[<3>] eye, Real[<3>] target, Real[<3>] up) => matrix_look_at(Matrix4x4, eye, target, up);
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fn Matrix2x2 Matrix2x2.transpose(&self)
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{
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return {
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self.m00, self.m10,
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self.m01, self.m11
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};
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}
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fn Matrix3x3 Matrix3x3.transpose(&self)
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{
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return {
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self.m00, self.m10, self.m20,
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self.m01, self.m11, self.m21,
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self.m02, self.m12, self.m22,
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};
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}
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fn Matrix4x4 Matrix4x4.transpose(&self)
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{
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return {
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self.m00, self.m10, self.m20, self.m30,
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self.m01, self.m11, self.m21, self.m31,
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self.m02, self.m12, self.m22, self.m32,
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self.m03, self.m13, self.m23, self.m33,
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};
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}
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fn Real Matrix2x2.determinant(&self)
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{
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return self.m00 * self.m11 - self.m01 * self.m10;
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}
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fn Real Matrix3x3.determinant(&self)
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{
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return
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self.m00 * (self.m11 * self.m22 - self.m21 * self.m12) -
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self.m01 * (self.m10 * self.m22 - self.m20 * self.m12) +
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self.m02 * (self.m10 * self.m21 - self.m20 * self.m11);
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}
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fn Real Matrix4x4.determinant(&self)
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{
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return
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self.m00 * (self.m11 * (self.m22 * self.m33 - self.m32 * self.m23) -
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self.m12 * (self.m21 * self.m33 - self.m31 * self.m23) +
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self.m13 * (self.m21 * self.m32 - self.m31 * self.m22) ) -
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self.m01 * (self.m10 * (self.m22 * self.m33 - self.m32 * self.m23) -
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self.m12 * (self.m20 * self.m33 - self.m30 * self.m23) +
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self.m13 * (self.m20 * self.m32 - self.m30 * self.m22) ) +
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self.m02 * (self.m10 * (self.m21 * self.m33 - self.m31 * self.m23) -
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self.m11 * (self.m20 * self.m33 - self.m30 * self.m23) +
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self.m13 * (self.m20 * self.m31 - self.m30 * self.m21) ) -
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self.m03 * (self.m10 * (self.m21 * self.m32 - self.m31 * self.m22) -
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self.m11 * (self.m20 * self.m32 - self.m30 * self.m22) +
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self.m12 * (self.m20 * self.m31 - self.m30 * self.m21) );
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}
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fn Matrix2x2 Matrix2x2.adjoint(&self)
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{
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return { self.m11, -self.m01, -self.m10, self.m00 };
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}
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fn Matrix3x3 Matrix3x3.adjoint(&self)
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{
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return {
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(self.m11 * self.m22 - self.m21 * self.m12),
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-(self.m10 * self.m22 - self.m20 * self.m12),
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(self.m10 * self.m21 - self.m20 * self.m11),
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-(self.m01 * self.m22 - self.m21 * self.m02),
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(self.m00 * self.m22 - self.m20 * self.m02),
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-(self.m00 * self.m21 - self.m20 * self.m01),
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(self.m01 * self.m12 - self.m11 * self.m02),
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-(self.m00 * self.m12 - self.m10 * self.m02),
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(self.m00 * self.m11 - self.m10 * self.m01),
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};
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}
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fn Matrix4x4 Matrix4x4.adjoint(&self)
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{
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return {
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(self.m11 * (self.m22 * self.m33 - self.m32 * self.m23) -
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self.m12 * (self.m21 * self.m33 - self.m31 * self.m23) +
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self.m13 * (self.m21 * self.m32 - self.m31 * self.m22)),
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-(self.m10 * (self.m22 * self.m33 - self.m32 * self.m23) -
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self.m12 * (self.m20 * self.m33 - self.m30 * self.m23) +
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self.m13 * (self.m20 * self.m32 - self.m30 * self.m22)),
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(self.m10 * (self.m21 * self.m33 - self.m31 * self.m23) -
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self.m11 * (self.m20 * self.m33 - self.m30 * self.m23) +
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self.m13 * (self.m20 * self.m31 - self.m30 * self.m21)),
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-(self.m10 * (self.m21 * self.m32 - self.m31 * self.m22) -
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self.m11 * (self.m20 * self.m32 - self.m30 * self.m22) +
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self.m12 * (self.m20 * self.m31 - self.m30 * self.m21)),
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-(self.m01 * (self.m22 * self.m33 - self.m32 * self.m23) -
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self.m02 * (self.m21 * self.m33 - self.m31 * self.m23) +
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self.m03 * (self.m21 * self.m32 - self.m31 * self.m22)),
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(self.m00 * (self.m22 * self.m33 - self.m32 * self.m23) -
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self.m02 * (self.m20 * self.m33 - self.m30 * self.m23) +
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self.m03 * (self.m20 * self.m32 - self.m30 * self.m22)),
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-(self.m00 * (self.m21 * self.m33 - self.m31 * self.m23) -
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self.m01 * (self.m20 * self.m33 - self.m30 * self.m23) +
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self.m03 * (self.m20 * self.m31 - self.m30 * self.m21)),
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(self.m00 * (self.m21 * self.m32 - self.m31 * self.m22) -
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self.m01 * (self.m20 * self.m32 - self.m30 * self.m22) +
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self.m02 * (self.m20 * self.m31 - self.m30 * self.m21)),
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(self.m01 * (self.m12 * self.m33 - self.m32 * self.m13) -
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self.m02 * (self.m11 * self.m33 - self.m31 * self.m13) +
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self.m03 * (self.m11 * self.m32 - self.m31 * self.m12)),
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-(self.m00 * (self.m12 * self.m33 - self.m32 * self.m13) -
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self.m02 * (self.m10 * self.m33 - self.m30 * self.m13) +
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self.m03 * (self.m10 * self.m32 - self.m30 * self.m12)),
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(self.m00 * (self.m11 * self.m33 - self.m31 * self.m13) -
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self.m01 * (self.m10 * self.m33 - self.m30 * self.m13) +
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self.m03 * (self.m10 * self.m31 - self.m30 * self.m11)),
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-(self.m00 * (self.m11 * self.m32 - self.m31 * self.m12) -
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self.m01 * (self.m10 * self.m32 - self.m30 * self.m12) +
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self.m02 * (self.m10 * self.m31 - self.m30 * self.m11)),
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-(self.m01 * (self.m12 * self.m23 - self.m22 * self.m13) -
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self.m02 * (self.m11 * self.m23 - self.m21 * self.m13) +
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self.m03 * (self.m11 * self.m22 - self.m21 * self.m12)),
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(self.m00 * (self.m12 * self.m23 - self.m22 * self.m13) -
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self.m02 * (self.m10 * self.m23 - self.m20 * self.m13) +
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self.m03 * (self.m10 * self.m22 - self.m20 * self.m12)),
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-(self.m00 * (self.m11 * self.m23 - self.m21 * self.m13) -
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self.m01 * (self.m10 * self.m23 - self.m20 * self.m13) +
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self.m03 * (self.m10 * self.m21 - self.m20 * self.m11)),
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(self.m00 * (self.m11 * self.m22 - self.m21 * self.m12) -
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self.m01 * (self.m10 * self.m22 - self.m20 * self.m12) +
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self.m02 * (self.m10 * self.m21 - self.m20 * self.m11)),
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};
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}
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fn Matrix2x2! Matrix2x2.inverse(&self)
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{
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Real det = self.determinant();
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if (det == 0) return MatrixError.MATRIX_INVERSE_DOESNT_EXIST?;
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Matrix2x2 adj = self.adjoint();
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return adj.component_mul(1 / det).transpose();
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}
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fn Matrix3x3! Matrix3x3.inverse(&self)
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{
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Real det = self.determinant();
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if (det == 0) return MatrixError.MATRIX_INVERSE_DOESNT_EXIST?;
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Matrix3x3 adj = self.adjoint();
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return adj.component_mul(1 / det).transpose();
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}
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fn Matrix4x4! Matrix4x4.inverse(&self)
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{
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Real det = self.determinant();
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if (det == 0) return MatrixError.MATRIX_INVERSE_DOESNT_EXIST?;
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Matrix4x4 adj = self.adjoint();
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return adj.component_mul(1 / det).transpose();
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}
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fn Matrix3x3 Matrix3x3.translate(&self, Real[<2>] v)
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{
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return self.mul({
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1, 0, v[0],
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0, 1, v[1],
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0, 0, 1,
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});
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}
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fn Matrix4x4 Matrix4x4.translate(&self, Real[<3>] v)
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{
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return self.mul({
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1, 0, 0, v[0],
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0, 1, 0, v[1],
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0, 0, 1, v[2],
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0, 0, 0, 1,
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});
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}
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// r in radians
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fn Matrix3x3 Matrix3x3.rotate(&self, Real r)
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{
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return self.mul({
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math::cos(r), -math::sin(r), 0,
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math::sin(r), math::cos(r), 0,
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0, 0, 1,
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});
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}
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// r in radians
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fn Matrix4x4 Matrix4x4.rotate_z(&self, Real r)
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{
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return self.mul({
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math::cos(r), -math::sin(r), 0, 0,
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math::sin(r), math::cos(r), 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1,
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});
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}
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// r in radians
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fn Matrix4x4 Matrix4x4.rotate_y(&self, Real r)
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{
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return self.mul({
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math::cos(r), 0, -math::sin(r), 0,
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0, 1, 0, 0,
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math::sin(r), 0, math::cos(r), 0,
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0, 0, 0, 1,
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});
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}
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// r in radians
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fn Matrix4x4 Matrix4x4.rotate_x(&self, Real r)
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{
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return self.mul({
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1, 0, 0, 0,
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0, math::cos(r), -math::sin(r), 0,
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0, math::sin(r), math::cos(r), 0,
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0, 0, 0, 1,
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});
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}
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fn Matrix3x3 Matrix3x3.scale(&self, Real[<2>] v)
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{
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return self.mul({
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v[0], 0, 0,
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0, v[1], 0,
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0, 0, 1,
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});
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}
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fn Real Matrix2x2.trace(&self) => self.m00 + self.m11;
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fn Real Matrix3x3.trace(&self) => self.m00 + self.m11 + self.m22;
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fn Real Matrix4x4.trace(&self) => self.m00 + self.m11 + self.m22 + self.m33;
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fn Matrix4x4 Matrix4x4.scale(&self, Real[<3>] v)
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{
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return self.mul({
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v[0], 0, 0, 0,
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0, v[1], 0, 0,
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0, 0, v[2], 0,
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0, 0, 0, 1,
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});
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}
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fn Matrix4x4 ortho(Real left, Real right, Real top, Real bottom, Real near, Real far)
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{
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Real width = right - left;
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Real height = top - bottom;
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Real depth = far - near;
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return {
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2 / width, 0, 0, 0,
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0, 2 / height, 0, 0,
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0, 0, -2 / depth, 0,
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-(right + left) / width, -(top + bottom) / height, -(far + near) / depth, 1
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};
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}
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|
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// fov in radians
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fn Matrix4x4 perspective(Real fov, Real aspect_ratio, Real near, Real far)
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{
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Real f = (Real)math::tan(math::PI * 0.5 - 0.5 * fov);
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Real range_inv = (Real)1.0 / (near - far);
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|
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return {
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f / aspect_ratio, 0, 0, 0,
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0, f, 0, 0,
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0, 0, (near + far) * range_inv, near * far * range_inv * 2,
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|
0, 0, -1, 0,
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};
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}
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|
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const Matrix2x2 IDENTITY2 = { .m = { [0] = 1, [3] = 1 } };
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const Matrix3x3 IDENTITY3 = { .m = { [0] = 1, [4] = 1, [8] = 1 } };
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const Matrix4x4 IDENTITY4 = { .m = { [0] = 1, [5] = 1, [10] = 1, [15] = 1 } };
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|
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macro matrix_component_mul(mat, val) @private
|
|
{
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|
var $Type = Real[<$typeof(mat.m).len>];
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return $typeof(*mat) { .m = val * ($Type)mat.m };
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|
}
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|
|
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macro matrix_add(mat, mat2) @private
|
|
{
|
|
var $Type = Real[<$typeof(mat.m).len>];
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|
return $typeof(*mat) { .m = ($Type)mat.m + ($Type)mat2.m };
|
|
}
|
|
|
|
macro matrix_sub(mat, mat2) @private
|
|
{
|
|
var $Type = Real[<$typeof(mat.m).len>];
|
|
return $typeof(*mat) { .m = ($Type)mat.m - ($Type)mat2.m };
|
|
}
|
|
|
|
macro matrix_look_at($Type, eye, target, up) @private
|
|
{
|
|
var vz = (eye - target).normalize();
|
|
var vx = up.cross(vz).normalize();
|
|
var vy = vz.cross(vx);
|
|
|
|
return $Type {
|
|
vx[0], vx[1], vx[2], - (Real)vx.dot(eye),
|
|
vy[0], vy[1], vy[2], - (Real)vy.dot(eye),
|
|
vz[0], vz[1], vz[2], - (Real)vz.dot(eye),
|
|
0.0, 0.0, 0.0, 1
|
|
};
|
|
}
|