mat2

Header: cglm/mat2.h

Table of contents (click to go):

Macros:

1. GLM_MAT2_IDENTITY_INIT

2. GLM_MAT2_ZERO_INIT

3. GLM_MAT2_IDENTITY

4. GLM_MAT2_ZERO

Functions:

1. glm_mat2_make()

2. glm_mat2_copy()

3. glm_mat2_identity()

4. glm_mat2_identity_array()

5. glm_mat2_zero()

6. glm_mat2_mul()

7. glm_mat2_mulv()

8. glm_mat2_transpose_to()

9. glm_mat2_transpose()

10. glm_mat2_scale()

11. glm_mat2_inv()

12. glm_mat2_swap_col()

13. glm_mat2_swap_row()

14. glm_mat2_det()

15. glm_mat2_trace()

16. glm_mat2_rmc()

Represented

mat2x2

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

Functions documentation

void glm_mat2_make(const float *__restrict src, mat2 dest)

Create mat2 (dest) from pointer (src).

Note

@src must contain at least 4 elements.

Parameters:

[in] src pointer to an array of floats (left)

[out] dest destination (result, mat2)

Note

Mathematical explanation

float array (1x4) (src)

	column 1
row 1	v0
row 2	v1
row 3	v2
row 4	v3

mat2 (dest)

	column 1	column 2
row 1	v0	v2
row 2	v1	v3

Note

Example

mat2 dest = GLM_MAT2_ZERO_INIT;
float src[4] = { 1.00, 5.00, 8.00, 11.00 };
glm_mat2_make(src, dest);

float array (1x4) (src)

	column 1
row 1	1.00
row 2	5.00
row 3	8.00
row 4	11.00

mat2 (dest) Before

	column 1	column 2
row 1	0.00	0.00
row 2	0.00	0.00

mat2 (dest) After

	column 1	column 2
row 1	1.00	8.00
row 2	5.00	11.00

void glm_mat2_copy(mat2 mat, mat2 dest)

Copy mat2 (mat) to mat2 (dest).

Parameters:

[in] mat mat2 (left,src)

[out] dest destination (result, mat2)

Note

Mathematical explanation

mat2 (mat)

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

mat2 (dest)

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

Note

Example

mat2 mat = {{3.00,4.00},{7.00,8.00}};
mat2 dest = GLM_MAT2_ZERO_INIT;
glm_mat2_copy(mat, dest);

mat2 (mat)

	column 1	column 2
row 1	3.00	7.00
row 2	4.00	8.00

mat2 (dest) Before

	column 1	column 2
row 1	0.00	0.00
row 2	0.00	0.00

mat2 (dest) After

	column 1	column 2
row 1	3.00	7.00
row 2	4.00	8.00

void glm_mat2_identity(mat2 m)

Copy a mat2 identity to mat2 (m), or makes mat2 (m) an identity.

The same thing may be achieved with either of bellow methods,

but it is more easy to do that with this func especially for members

e.g. glm_mat2_identity(aStruct->aMatrix);.

glm_mat2_copy(GLM_MAT2_IDENTITY, m);

// or
mat2 mat = GLM_MAT2_IDENTITY_INIT;

Parameters:

[in, out] m mat2 (src, dest)

Note

Mathematical explanation

mat2 (m)

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

mat2 (m)

	column 1	column 2
row 1	1.00	0.00
row 2	0.00	1.00

Note

Example

mat2 m = {{3.00,4.00},{7.00,8.00}};
glm_mat2_identity(m);

mat2 (m)

	column 1	column 2
row 1	3.00	7.00
row 2	4.00	8.00

mat2 (m)

	column 1	column 2
row 1	1.00	0.00
row 2	0.00	1.00

void glm_mat2_identity_array(mat2 *__restrict mats, size_t count)

Given an array of mat2’s (mats) make each matrix an identity matrix.

Parameters:

[in, out] mats Array of mat2’s (must be aligned (16/32) if alignment is not disabled)

[in] count Array size of mats or number of matrices

Note

Mathematical explanation

mat2 (mats[index])

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

mat2 (mats[index])

	column 1	column 2
row 1	1.00	0.00
row 2	0.00	1.00

Note

Example

size_t count = 3;

mat2 matrices[count] = {
    {{1.00,2.00},{5.00,6.00}},
    {{3.00,4.00},{7.00,8.00}},
    {{5.00,6.00},{9.00,10.00}},
};

glm_mat2_identity_array(matrices, count);

mat2 (mats[0]) Before

	column 1	column 2
row 1	1.00	5.00
row 2	2.00	6.00

mat2 (mats[0]) After

	column 1	column 2
row 1	1.00	0.00
row 2	0.00	1.00

mat2 (mats[1]) Before

	column 1	column 2
row 1	3.00	7.00
row 2	4.00	8.00

mat2 (mats[1]) After

	column 1	column 2
row 1	1.00	0.00
row 2	0.00	1.00

mat2 (mats[2]) Before

	column 1	column 2
row 1	5.00	9.00
row 2	6.00	10.00

mat2 (mats[2]) After

	column 1	column 2
row 1	1.00	0.00
row 2	0.00	1.00

void glm_mat2_zero(mat2 m)

Zero out the mat2 (m).

Parameters:

[in, out] m mat2 (src, dest)

Note

Mathematical explanation

mat2 (m)

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

mat2 (m)

	column 1	column 2
row 1	0.00	0.00
row 2	0.00	0.00

Note

Example

mat2 m = {{19.00,5.00},{2.00,4.00}};
glm_mat2_zero(m);

mat2 (m) Before

	column 1	column 2
row 1	19.00	2.00
row 2	5.00	4.00

mat2 (m) After

	column 1	column 2
row 1	0.00	0.00
row 2	0.00	0.00

void glm_mat2_mul(mat2 m1, mat2 m2, mat2 dest)

Multiply mat2 (m1) by mat2 (m2) and store in mat2 (dest).

m1, m2 and dest matrices can be same matrix, it is possible to write this:

mat2 m = GLM_MAT2_IDENTITY_INIT;
glm_mat2_mul(m, m, m);

Parameters:

[in] m1 mat2 (left)

[in] m2 mat2 (right)

[out] dest destination (result, mat2)

Note

Mathematical explanation

mat2 (m1)

	column 1	column 2
row 1	a00	a10
row 2	a01	a11

mat2 (m2)

	column 1	column 2
row 1	b00	b10
row 2	b01	b11

mat2 (dest)

	column 1	column 2
row 1	a00 * b00 + a10 * b01	a00 * b10 + a10 * b11
row 2	a01 * b00 + a11 * b01	a01 * b10 + a11 * b11

Note

Example

mat2 m = {{19.00,5.00},{2.00,4.00}};
glm_mat2_mul(m, m, m);

mat2 (m1)

	column 1	column 2
row 1	19.00	2.00
row 2	5.00	4.00

mat2 (m2)

	column 1	column 2
row 1	19.00	2.00
row 2	5.00	4.00

mat2 (dest)

	column 1	column 2
row 1	371.00 = 19.00 * 19.00 + 2.00 * 5.00	46.00 = 19.00 * 2.00 + 2.00 * 4.00
row 2	115.00 = 5.00 * 19.00 + 4.00 * 5.00	18.00 = 5.00 * 2.00 + 4.00 * 4.00

void glm_mat2_mulv(mat2 m, vec2 v, vec2 dest)

Multiply mat2 (m) by vec2 (v) and store in vec2 (dest).

Parameters:

[in] m mat2 (left)

[in] v vec2 (right, column vector)

[out] dest destination (result, column vector)

Note

Mathematical explanation

mat2 (m)

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

column vec2 (1x2) (v)

	column 1
row 1	v0
row 2	v1

column vec2 (1x2) (dest)

	column 1
row 1	m00 * v0 + m10 * v1
row 2	m01 * v0 + m11 * v1

Note

Example

vec2 dest;
vec2 v = {33.00,55.00};
mat2 m = {{1.00,2.00},{3.00,4.00}};
glm_mat2_mulv(m, v, dest);

mat2 (m)

	column 1	column 2
row 1	1.00	3.00
row 2	2.00	4.00

column vec2 (v)

	column 1
row 1	33.00
row 2	55.00

vec2 (dest) Result

	column 1
row 1	198.00 = 1.00 * 33.00 + 3.00 * 55.00
row 2	286.00 = 2.00 * 33.00 + 4.00 * 55.00

void glm_mat2_transpose_to(mat2 mat, mat2 dest)

Transpose mat2 (mat) and store in mat2 (dest).

Parameters:

[in] mat mat2 (left,src)

[out] dest destination (result, mat2)

Note

Mathematical explanation

mat2 (mat)

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

mat2 (dest)

	column 1	column 2
row 1	m00	m01
row 2	m10	m11

Note

Example

mat2 mat = {{1.00,2.00},{3.00,4.00}};
mat2 dest = GLM_MAT2_ZERO_INIT;
glm_mat2_transpose_to(mat, dest);

mat2 (mat)

	column 1	column 2
row 1	1.00	3.00
row 2	2.00	4.00

mat2 (dest) Before

	column 1	column 2
row 1	0.00	0.00
row 2	0.00	0.00

mat2 (dest) After

	column 1	column 2
row 1	1.00	2.00
row 2	3.00	4.00

void glm_mat2_transpose(mat2 m)

Transpose mat2 (m) and store result in the same matrix.

Parameters:

[in, out] m mat2 (src, dest)

Note

Mathematical explanation

mat2 (m) src

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

mat2 (m) dest

	column 1	column 2
row 1	m00	m01
row 2	m10	m11

Note

Example

mat2 m = {{1.00,2.00},{3.00,4.00}};
glm_mat2_transpose(m);

mat2 (m) Before

	column 1	column 2
row 1	1.00	3.00
row 2	2.00	4.00

mat2 (m) After

	column 1	column 2
row 1	1.00	2.00
row 2	3.00	4.00

void glm_mat2_scale(mat2 m, float s)

Multiply mat2 (m) by scalar constant (s).

Parameters:

[in, out] m mat2 (src, dest)

[in] s float (scalar)

Note

Mathematical explanation

mat2 (m)

	column 1	column 2
row 1	m00 * s	m10 * s
row 2	m01 * s	m11 * s

Note

Example

float s = 3.00f;
mat2 m = {{1.00,2.00},{3.00,4.00}};
glm_mat2_scale(m, s);

mat2 (m) Before

	column 1	column 2
row 1	1.00	3.00
row 2	2.00	4.00

mat2 (m) After

	column 1	column 2
row 1	3.00 = 1.00 * 3.00	9.00 = 3.00 * 3.00
row 2	6.00 = 2.00 * 3.00	12.00 = 4.00 * 3.00

void glm_mat2_inv(mat2 mat, mat2 dest)

Inverse mat2 (mat) and store in mat2 (dest).

Parameters:

[in] mat mat2 (left,src)

[out] dest destination (result, inverse mat2)

Note

Mathematical explanation

mat2 (mat)

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

mat2 (dest)

	column 1	column 2
row 1	m11 * (1.0f / (m00 * m11 - m01 * m10))	-m10 * (1.0f / (m00 * m11 - m01 * m10))
row 2	-m01 * (1.0f / (m00 * m11 - m01 * m10))	m00 * (1.0f / (m00 * m11 - m01 * m10))

Note

Example

mat2 dest = GLM_MAT2_ZERO_INIT;
mat2 mat = {{1.00,2.00},{3.00,4.00}};
glm_mat2_inv(mat, dest);

mat2 (mat) Before

	column 1	column 2
row 1	1.00	3.00
row 2	2.00	4.00

mat2 (dest) After

	column 1	column 2
row 1	-2.00 = 4.00 * (1.00 / (1.00 * 4.00 - 2.00 * 3.00))	1.50 = -3.00 * (1.00 / (1.00 * 4.00 - 2.00 * 3.00))
row 2	1.00 = -2.00 * (1.00 / (1.00 * 4.00 - 2.00 * 3.00))	-0.50 = 1.00 * (1.00 / (1.00 * 4.00 - 2.00 * 3.00))

void glm_mat2_swap_col(mat2 mat, int col1, int col2)

Swap two columns in mat2 (mat) and store in same matrix.

Parameters:

[in, out] mat mat2 (src, dest)

[in] col1 Column 1 array index

[in] col2 Column 2 array index

Note

Mathematical explanation

mat2 (mat) Before

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

glm_mat2_swap_col(mat, 0, 1);

mat2 (mat) After

	column 1	column 2
row 1	m10	m00
row 2	m11	m01

Note

Example

mat2 mat = {{76.00,5.00},{3.00,6.00}};
glm_mat2_swap_col(mat, 0, 1);

mat2 (mat) Before

	column 1	column 2
row 1	76.00	3.00
row 2	5.00	6.00

mat2 (mat) After

	column 1	column 2
row 1	3.00	76.00
row 2	6.00	5.00

void glm_mat2_swap_row(mat2 mat, int row1, int row2)

Swap two rows in mat2 (mat) and store in same matrix.

Parameters:

[in, out] mat mat2 (src, dest)

[in] row1 Row 1 array index

[in] row2 Row 2 array index

Note

Mathematical explanation

mat2 (mat) Before

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

glm_mat2_swap_row(mat, 0, 1);

mat2 (mat) After

	column 1	column 2
row 1	m01	m11
row 2	m00	m10

Note

Example

mat2 mat = {{76.00,5.00},{3.00,6.00}};
glm_mat2_swap_row(mat, 0, 1);

mat2 (mat) Before

	column 1	column 2
row 1	76.00	3.00
row 2	5.00	6.00

mat2 (mat) After

	column 1	column 2
row 1	5.00	6.00
row 2	76.00	3.00

float glm_mat2_det(mat2 m)

Returns mat2 determinant.

Parameters:

[in] m mat2 (src)

Returns:

mat2 determinant (float)

Note

Mathematical explanation

mat2 (m)

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

m00 * m11 - m10 * m01;

Note

Example

mat2 m = {{76.00,5.00},{3.00,6.00}};
glm_mat2_det(m);

mat2 (m)

	column 1	column 2
row 1	76.00	3.00
row 2	5.00	6.00

441.00 = 76.00 * 6.00 - 3.00 * 5.00;

void glm_mat2_trace(mat2 m)

Returns trace of matrix. Which is:

The sum of the elements on the main diagonal from

upper left corner to the bottom right corner.

Parameters:

[in] m mat2 (src)

Returns:

mat2 trace (float)

Note

Mathematical explanation

mat2 (m)

	column 1	column 2
row 1	m00	m10
row 2	m01	m11

m00 + m11;

Note

Example

mat2 m = {{76.00,5.00},{3.00,6.00}};
glm_mat2_trace(m);

mat2 (m)

	column 1	column 2
row 1	76.00	3.00
row 2	5.00	6.00

82.00 = 76.00 + 6.00;

float glm_mat2_rmc(vec2 r, mat2 m, vec2 c)

Helper for R (row vector) * M (matrix) * C (column vector)

rmc stands for Row * Matrix * Column

the result is scalar because M * C = ResC (1x2, column vector),

then if you take the dot_product(R (2x1), ResC (1x2)) = scalar value.

Parameters:

[in] r vec2 (2x1, row vector)

[in] m mat2 (2x2, matrix)

[in] c vec2 (1x2, column vector)

Returns:

Scalar value (float, 1x1)

Note

Mathematical explanation

row vec2 (2x1) (r)

	column 1	column 2
row 1	a00	a10

mat2 (m)

	column 1	column 2
row 1	b00	b10
row 2	b01	b11

column vec2 (1x2) (c)

	column 1
row 1	c00
row 2	c01

M * C = C (column vector)
dot_product(R, C)

column vec2 (1x2) (C)

	column 1
row 1	b00 * c00 + b10 * c01
row 2	b01 * c00 + b11 * c01

float (scalar)

	column 1
row 1	a00 * (b00 * c00 + b10 * c01) + a10 * (b01 * c00 + b11 * c01)

Note

Example

vec2 r = {8.00,4.00};
vec2 c = {7.00,2.00};
mat2 m = {{5.00,9.00},{3.00,6.00}};
glm_mat2_rmc(r, m, c);

row vec2 (2x1) (r)

	column 1	column 2
row 1	8.00	4.00

mat2 (m)

	column 1	column 2
row 1	5.00	3.00
row 2	9.00	6.00

column vec2 (1x2) (c)

	column 1
row 1	7.00
row 2	2.00

column vec2 (1x2) (C)

	column 1
row 1	41.00 = 5.00 * 7.00 + 3.00 * 2.00
row 2	75.00 = 9.00 * 7.00 + 6.00 * 2.00

float (1x1) (scalar)

	column 1
row 1	628.00 = 8.00 * 41.00 + 4.00 * 75.00