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cglm/docs/source/mat2.rst
Vincent Davis Jr 5d530cd8e0 mat2: add tables to docs & fix comments
Signed-off-by: Vincent Davis Jr <vince@underview.tech>
2025-04-11 00:13:54 -04:00

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.. default-domain:: C
mat2
====
Header: cglm/mat2.h
Table of contents (click to go):
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Macros:
1. GLM_MAT2_IDENTITY_INIT
#. GLM_MAT2_ZERO_INIT
#. GLM_MAT2_IDENTITY
#. GLM_MAT2_ZERO
Functions:
1. :c:func:`glm_mat2_make`
#. :c:func:`glm_mat2_copy`
#. :c:func:`glm_mat2_identity`
#. :c:func:`glm_mat2_identity_array`
#. :c:func:`glm_mat2_zero`
#. :c:func:`glm_mat2_mul`
#. :c:func:`glm_mat2_mulv`
#. :c:func:`glm_mat2_transpose_to`
#. :c:func:`glm_mat2_transpose`
#. :c:func:`glm_mat2_scale`
#. :c:func:`glm_mat2_inv`
#. :c:func:`glm_mat2_swap_col`
#. :c:func:`glm_mat2_swap_row`
#. :c:func:`glm_mat2_det`
#. :c:func:`glm_mat2_trace`
#. :c:func:`glm_mat2_rmc`
Represented
~~~~~~~~~~~
.. csv-table:: mat2x2
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
Functions documentation
~~~~~~~~~~~~~~~~~~~~~~~
.. c:function:: 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
.. csv-table:: float array (1x4) **(src)**
:header: "", "column 1"
"row 1", "v0"
"row 2", "v1"
"row 3", "v2"
"row 4", "v3"
.. csv-table:: mat2 **(dest)**
:header: "", "column 1", "column 2"
"row 1", "v0", "v2"
"row 2", "v1", "v3"
.. note:: Example
.. code-block:: c
mat2 dest = GLM_MAT2_ZERO_INIT;
float src[4] = { 1.00, 5.00, 8.00, 11.00 };
glm_mat2_make(src, dest);
.. csv-table:: float array (1x4) **(src)**
:header: "", "column 1"
"row 1", "1.00"
"row 2", "5.00"
"row 3", "8.00"
"row 4", "11.00"
.. csv-table:: mat2 **(dest)** Before
:header: "", "column 1", "column 2"
"row 1", "0.00", "0.00"
"row 2", "0.00", "0.00"
.. csv-table:: mat2 **(dest)** After
:header: "", "column 1", "column 2"
"row 1", "1.00", "8.00"
"row 2", "5.00", "11.00"
.. c:function:: void glm_mat2_copy(mat2 mat, mat2 dest)
Copy mat2 (mat) to mat2 (dest).
Parameters:
| *[in]* **mat** mat2 (left)
| *[out]* **dest** destination (result, mat2)
.. note:: Mathematical explanation
.. csv-table:: mat2 **(mat)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. csv-table:: mat2 **(dest)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. note:: Example
.. code-block:: c
mat2 mat = {{3.00,4.00},{7.00,8.00}};
mat2 dest = GLM_MAT2_ZERO_INIT;
glm_mat2_copy(mat, dest);
.. csv-table:: mat2 **(mat)**
:header: "", "column 1", "column 2"
"row 1", "3.00", "7.00"
"row 2", "4.00", "8.00"
.. csv-table:: mat2 **(dest)** Before
:header: "", "column 1", "column 2"
"row 1", "0.00", "0.00"
"row 2", "0.00", "0.00"
.. csv-table:: mat2 **(dest)** After
:header: "", "column 1", "column 2"
"row 1", "3.00", "7.00"
"row 2", "4.00", "8.00"
.. c:function:: 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);``.
.. code-block:: c
glm_mat2_copy(GLM_MAT2_IDENTITY, m);
// or
mat2 mat = GLM_MAT2_IDENTITY_INIT;
Parameters:
| *[in, out]* **m** mat2 (src, dest)
.. note:: Mathematical explanation
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "1.00", "0.00"
"row 2", "0.00", "1.00"
.. note:: Example
.. code-block:: c
mat2 m = {{3.00,4.00},{7.00,8.00}};
glm_mat2_identity(m);
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "3.00", "7.00"
"row 2", "4.00", "8.00"
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "1.00", "0.00"
"row 2", "0.00", "1.00"
.. c:function:: 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
.. csv-table:: mat2 **(mats[index])**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. csv-table:: mat2 **(mats[index])**
:header: "", "column 1", "column 2"
"row 1", "1.00", "0.00"
"row 2", "0.00", "1.00"
.. note:: Example
.. code-block:: c
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);
.. csv-table:: mat2 **(mats[0])** Before
:header: "", "column 1", "column 2"
"row 1", "1.00", "5.00"
"row 2", "2.00", "6.00"
.. csv-table:: mat2 **(mats[0])** After
:header: "", "column 1", "column 2"
"row 1", "1.00", "0.00"
"row 2", "0.00", "1.00"
.. csv-table:: mat2 **(mats[1])** Before
:header: "", "column 1", "column 2"
"row 1", "3.00", "7.00"
"row 2", "4.00", "8.00"
.. csv-table:: mat2 **(mats[1])** After
:header: "", "column 1", "column 2"
"row 1", "1.00", "0.00"
"row 2", "0.00", "1.00"
.. csv-table:: mat2 **(mats[2])** Before
:header: "", "column 1", "column 2"
"row 1", "5.00", "9.00"
"row 2", "6.00", "10.00"
.. csv-table:: mat2 **(mats[2])** After
:header: "", "column 1", "column 2"
"row 1", "1.00", "0.00"
"row 2", "0.00", "1.00"
.. c:function:: void glm_mat2_zero(mat2 m)
Zero out the mat2 (m).
Parameters:
| *[in, out]* **m** mat2 (src, dest)
.. note:: Mathematical explanation
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "0.00", "0.00"
"row 2", "0.00", "0.00"
.. note:: Example
.. code-block:: c
mat2 m = {{19.00,5.00},{2.00,4.00}};
glm_mat2_zero(m);
.. csv-table:: mat2 **(m)** Before
:header: "", "column 1", "column 2"
"row 1", "19.00", "2.00"
"row 2", "5.00", "4.00"
.. csv-table:: mat2 **(m)** After
:header: "", "column 1", "column 2"
"row 1", "0.00", "0.00"
"row 2", "0.00", "0.00"
.. c:function:: 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:
.. code-block:: c
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
.. csv-table:: mat2 **(m1)**
:header: "", "column 1", "column 2"
"row 1", "a00", "a10"
"row 2", "a01", "a11"
.. csv-table:: mat2 **(m2)**
:header: "", "column 1", "column 2"
"row 1", "b00", "b10"
"row 2", "b01", "b11"
.. csv-table:: mat2 **(dest)**
:header: "", "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
.. code-block:: c
mat2 m = {{19.00,5.00},{2.00,4.00}};
glm_mat2_mul(m, m, m);
.. csv-table:: mat2 **(m1)**
:header: "", "column 1", "column 2"
"row 1", "19.00", "2.00"
"row 2", "5.00", "4.00"
.. csv-table:: mat2 **(m2)**
:header: "", "column 1", "column 2"
"row 1", "19.00", "2.00"
"row 2", "5.00", "4.00"
.. csv-table:: mat2 **(dest)**
:header: "", "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"
.. c:function:: 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
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. csv-table:: column vec2 (1x2) **(v)**
:header: "", "column 1"
"row 1", "v0"
"row 2", "v1"
.. csv-table:: column vec2 (1x2) **(dest)**
:header: "", "column 1"
"row 1", "m00 * v0 + m10 * v1"
"row 2", "m01 * v0 + m11 * v1"
.. note:: Example
.. code-block:: c
vec2 dest;
vec2 v = {33.00,55.00};
mat2 m = {{1.00,2.00},{3.00,4.00}};
glm_mat2_mulv(m, v, dest);
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "1.00", "3.00"
"row 2", "2.00", "4.00"
.. csv-table:: column vec2 **(v)**
:header: "", "column 1"
"row 1", "33.00"
"row 2", "55.00"
.. csv-table:: vec2 **(dest)** Result
:header: "", "column 1"
"row 1", "**143.00** = 1.00 * 33.00 + 2.00 * 55.00"
"row 2", "**286.00** = 2.00 * 33.00 + 4.00 * 5.00"
.. c:function:: void glm_mat2_transpose_to(mat2 mat, mat2 dest)
Transpose mat2 (mat) and store in mat2 (dest).
Parameters:
| *[in]* **mat** mat2 (left)
| *[out]* **dest** destination (result, mat2)
.. note:: Mathematical explanation
.. csv-table:: mat2 **(mat)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. csv-table:: mat2 **(dest)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m01"
"row 2", "m10", "m11"
.. note:: Example
.. code-block:: c
mat2 mat = {{1.00,2.00},{3.00,4.00}};
mat2 dest = GLM_MAT2_ZERO_INIT;
glm_mat2_transpose_to(mat, dest);
.. csv-table:: mat2 **(mat)**
:header: "", "column 1", "column 2"
"row 1", "1.00", "3.00"
"row 2", "2.00", "4.00"
.. csv-table:: mat2 **(dest)** Before
:header: "", "column 1", "column 2"
"row 1", "0.00", "0.00"
"row 2", "0.00", "0.00"
.. csv-table:: mat2 **(dest)** After
:header: "", "column 1", "column 2"
"row 1", "1.00", "2.00"
"row 2", "3.00", "4.00"
.. c:function:: 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
.. csv-table:: mat2 **(m)** src
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. csv-table:: mat2 **(m)** dest
:header: "", "column 1", "column 2"
"row 1", "m00", "m01"
"row 2", "m10", "m11"
.. note:: Example
.. code-block:: c
mat2 m = {{1.00,2.00},{3.00,4.00}};
glm_mat2_transpose(m);
.. csv-table:: mat2 **(m)** Before
:header: "", "column 1", "column 2"
"row 1", "1.00", "3.00"
"row 2", "2.00", "4.00"
.. csv-table:: mat2 **(m)** After
:header: "", "column 1", "column 2"
"row 1", "1.00", "2.00"
"row 2", "3.00", "4.00"
.. c:function:: 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
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "m00 * s", "m10 * s"
"row 2", "m01 * s", "m11 * s"
.. note:: Example
.. code-block:: c
float s = 3.00f;
mat2 m = {{1.00,2.00},{3.00,4.00}};
glm_mat2_scale(m, s);
.. csv-table:: mat2 **(src)** Before
:header: "", "column 1", "column 2"
"row 1", "1.00", "3.00"
"row 2", "2.00", "4.00"
.. csv-table:: mat2 **(dest)** After
:header: "", "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"
.. c:function:: void glm_mat2_inv(mat2 mat, mat2 dest)
Inverse mat2 (mat) and store in mat2 (dest).
Parameters:
| *[in]* **mat** mat2 (left)
| *[out]* **dest** destination (result, inverse mat2)
.. note:: Mathematical explanation
.. csv-table:: mat2 **(mat)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. csv-table:: mat2 **(dest)**
:header: "", "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
.. code-block:: c
mat2 dest = GLM_MAT2_ZERO_INIT;
mat2 mat = {{1.00,2.00},{3.00,4.00}};
glm_mat2_inv(mat, dest);
.. csv-table:: mat2 **(mat)** Before
:header: "", "column 1", "column 2"
"row 1", "1.00", "3.00"
"row 2", "2.00", "4.00"
.. csv-table:: mat2 **(dest)** After
:header: "", "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))"
.. c:function:: 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
.. csv-table:: mat2 **(mat)** Before
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. code-block:: c
glm_mat2_swap_col(mat, 0, 1);
.. csv-table:: mat2 **(mat)** After
:header: "", "column 1", "column 2"
"row 1", "m10", "m00"
"row 2", "m11", "m01"
.. note:: Example
.. code-block:: c
mat2 mat = {{76.00,5.00},{3.00,6.00}};
glm_mat2_swap_col(mat, 0, 1);
.. csv-table:: mat2 **(mat)** Before
:header: "", "column 1", "column 2"
"row 1", "76.00", "3.00"
"row 2", "5.00", "6.00"
.. csv-table:: mat2 **(mat)** After
:header: "", "column 1", "column 2"
"row 1", "3.00", "76.00"
"row 2", "6.00", "5.00"
.. c:function:: 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
.. csv-table:: mat2 **(mat)** Before
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. code-block:: c
glm_mat2_swap_row(mat, 0, 1);
.. csv-table:: mat2 **(mat)** After
:header: "", "column 1", "column 2"
"row 1", "m01", "m11"
"row 2", "m00", "m10"
.. note:: Example
.. code-block:: c
mat2 mat = {{76.00,5.00},{3.00,6.00}};
glm_mat2_swap_row(mat, 0, 1);
.. csv-table:: mat2 **(mat)** Before
:header: "", "column 1", "column 2"
"row 1", "76.00", "3.00"
"row 2", "5.00", "6.00"
.. csv-table:: mat2 **(mat)** After
:header: "", "column 1", "column 2"
"row 1", "5.00", "6.00"
"row 2", "76.00", "3.00"
.. c:function:: float glm_mat2_det(mat2 m)
Returns mat2 determinant.
Parameters:
| *[in]* **m** mat2 (src)
Returns:
| mat2 determinant (float)
.. note:: Mathematical explanation
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. code-block:: c
m00 * m11 - m10 * m01;
.. note:: Example
.. code-block:: c
mat2 m = {{76.00,5.00},{3.00,6.00}};
glm_mat2_det(m);
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "76.00", "3.00"
"row 2", "5.00", "6.00"
.. code-block:: c
441.00 = 76.00 * 6.00 - 3.00 * 5.00;
.. c:function:: 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
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "m00", "m10"
"row 2", "m01", "m11"
.. code-block:: c
m00 + m11;
.. note:: Example
.. code-block:: c
mat2 m = {{76.00,5.00},{3.00,6.00}};
glm_mat2_trace(m);
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "76.00", "3.00"
"row 2", "5.00", "6.00"
.. code-block:: c
82.00 = 76.00 + 6.00;
.. c:function:: 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
.. csv-table:: row vec2 (2x1) **(r)**
:header: "", "column 1", "column 2"
"row 1", "a00", "a10"
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "b00", "b10"
"row 2", "b01", "b11"
.. csv-table:: column vec2 (1x2) **(c)**
:header: "", "column 1"
"row 1", "c00"
"row 2", "c01"
.. code-block:: c
M * C = C (column vector)
dot_product(R, C)
.. csv-table:: column vec2 (1x2) **(C)**
:header: "", "column 1"
"row 1", "b00 * c00 + b10 * c01"
"row 2", "b01 * c00 + b11 * c01"
.. csv-table:: float **(scalar)**
:header: "", "column 1"
"row 1", "a00 * (b00 * c00 + b10 * c01) + a10 * (b01 * c00 + b11 * c01)"
.. note:: Example
.. code-block:: c
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);
.. csv-table:: row vec2 (2x1) **(r)**
:header: "", "column 1", "column 2"
"row 1", "8.00", "4.00"
.. csv-table:: mat2 **(m)**
:header: "", "column 1", "column 2"
"row 1", "5.00", "3.00"
"row 2", "9.00", "6.00"
.. csv-table:: column vec2 (1x2) **(c)**
:header: "", "column 1"
"row 1", "7.00"
"row 2", "2.00"
.. csv-table:: column vec2 (1x2) **(C)**
:header: "", "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"
.. csv-table:: float (1x1) **(scalar)**
:header: "", "column 1"
"row 1", "**628.00** = 8.00 * 41.00 + 4.00 * 75.00"