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cglm/docs/source/mat3.rst
Vincent Davis Jr 6f5fde8b52 mat3: add tables to docs & fix comments 
Signed-off-by: Vincent Davis Jr <vince@underview.tech>
2025-04-17 14:22:00 -04:00

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.. default-domain:: C
mat3
====
Header: cglm/mat3.h
Table of contents (click to go):
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Macros:
1. GLM_MAT3_IDENTITY_INIT
#. GLM_MAT3_ZERO_INIT
#. GLM_MAT3_IDENTITY
#. GLM_MAT3_ZERO
#. glm_mat3_dup(mat, dest)
Functions:
1. :c:func:`glm_mat3_make`
#. :c:func:`glm_mat3_copy`
#. :c:func:`glm_mat3_identity`
#. :c:func:`glm_mat3_identity_array`
#. :c:func:`glm_mat3_zero`
#. :c:func:`glm_mat3_mul`
#. :c:func:`glm_mat3_mulv`
#. :c:func:`glm_mat3_transpose_to`
#. :c:func:`glm_mat3_transpose`
#. :c:func:`glm_mat3_scale`
#. :c:func:`glm_mat3_inv`
#. :c:func:`glm_mat3_swap_col`
#. :c:func:`glm_mat3_swap_row`
#. :c:func:`glm_mat3_quat`
#. :c:func:`glm_mat3_textrans`
#. :c:func:`glm_mat3_det`
#. :c:func:`glm_mat3_trace`
#. :c:func:`glm_mat3_rmc`
Represented
~~~~~~~~~~~
.. csv-table:: mat3x3
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
Functions documentation
~~~~~~~~~~~~~~~~~~~~~~~
.. c:function:: void glm_mat3_make(const float * __restrict src, mat3 dest)
Create mat3 (dest) from pointer (src).
.. note:: **@src** must contain at least 9 elements.
Parameters:
| *[in]* **src** pointer to an array of floats (left)
| *[out]* **dest** destination (result, mat3)
.. note:: Mathematical explanation
.. csv-table:: float array (1x9) **(src)**
:header: "", "column 1"
"row 1", "v0"
"row 2", "v1"
"row 3", "v2"
"row 4", "v3"
"row 5", "v4"
"row 6", "v5"
"row 7", "v6"
"row 8", "v7"
"row 9", "v8"
.. csv-table:: mat3 **(dest)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "v0", "v3", "v6"
"row 2", "v1", "v4", "v7"
"row 3", "v2", "v5", "v8"
.. note:: Example
.. code-block:: c
float src[9] = {
1.00, 5.00, 8.00,
11.00, 42.00, 33.00,
95.00, 59.00, 88.00,
};
mat3 dest = GLM_MAT3_ZERO_INIT;
glm_mat3_make(src, dest);
.. csv-table:: float array (1x9) **(src)**
:header: "", "column 1"
"row 1", "1.00"
"row 2", "5.00"
"row 3", "8.00"
"row 4", "11.00"
"row 5", "42.00"
"row 6", "33.00"
"row 7", "95.00"
"row 8", "59.00"
"row 9", "88.00"
.. csv-table:: mat3 **(dest)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "0.00", "0.00", "0.00"
"row 2", "0.00", "0.00", "0.00"
"row 3", "0.00", "0.00", "0.00"
.. csv-table:: mat3 **(dest)** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "11.00", "95.00"
"row 2", "5.00", "42.00", "59.00"
"row 3", "8.00", "33.00", "88.00"
.. c:function:: void glm_mat3_copy(mat3 mat, mat3 dest)
Copy mat3 (mat) to mat3 (dest).
Parameters:
| *[in]* **mat** mat3 (left, src)
| *[out]* **dest** destination (result, mat3)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(mat)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. csv-table:: mat3 **(dest)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. note:: Example
.. code-block:: c
mat3 mat = {
{3.00,4.00,5.00},
{7.00,8.00,9.00},
{17.00,18.00,19.00},
};
mat3 dest = GLM_MAT2_ZERO_INIT;
glm_mat3_copy(mat, dest);
.. csv-table:: mat3 **(mat)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "3.00", "4.00", "5.00"
"row 2", "7.00", "8.00", "9.00"
"row 3", "17.00", "18.00", "19.00"
.. csv-table:: mat3 **(dest)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "0.00", "0.00", "0.00"
"row 2", "0.00", "0.00", "0.00"
"row 3", "0.00", "0.00", "0.00"
.. csv-table:: mat3 **(dest)** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "3.00", "4.00", "5.00"
"row 2", "7.00", "8.00", "9.00"
"row 3", "17.00", "18.00", "19.00"
.. c:function:: void glm_mat3_identity(mat3 m)
| Copy a mat3 identity to mat3 **(m)**, or makes mat3 **(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_mat3_identity(aStruct->aMatrix);``.
.. code-block:: c
glm_mat3_copy(GLM_MAT3_IDENTITY, m);
// or
mat3 mat = GLM_MAT3_IDENTITY_INIT;
Parameters:
| *[in, out]* **m** mat3 (src, dest)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "0.00", "0.00"
"row 2", "0.00", "1.00", "0.00"
"row 3", "0.00", "0.00", "1.00"
.. note:: Example
.. code-block:: c
mat3 m = {
{3.00,4.00,5.00},
{7.00,8.00,9.00},
{17.00,18.00,19.00},
};
glm_mat3_identity(m);
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "3.00", "4.00", "5.00"
"row 2", "7.00", "8.00", "9.00"
"row 3", "17.00", "18.00", "19.00"
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "0.00", "0.00"
"row 2", "0.00", "1.00", "0.00"
"row 3", "0.00", "0.00", "1.00"
.. c:function:: void glm_mat3_identity_array(mat3 * __restrict mats, size_t count)
Given an array of mat3's **(mats)** make each matrix an identity matrix.
Parameters:
| *[in, out]* **mats** Array of mat3'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:: mat3 **(mats[index])**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. csv-table:: mat3 **(mats[index])**
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "0.00", "0.00"
"row 2", "0.00", "1.00", "0.00"
"row 3", "0.00", "0.00", "1.00"
.. note:: Example
.. code-block:: c
size_t count = 3;
mat3 matrices[count] = {
{{1.00,2.00,3.00},{10.00,11.00,12.00},{19.00,20.00,21.00}},
{{4.00,5.00,6.00},{13.00,14.00,15.00},{22.00,23.00,24.00}},
{{7.00,8.00,9.00},{16.00,17.00,18.00},{25.00,26.00,27.00}},
};
glm_mat3_identity_array(matrices, count);
.. csv-table:: mat3 **(mats[0])** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "10.00", "19.00"
"row 2", "2.00", "11.00", "20.00"
"row 3", "3.00", "12.00", "21.00"
.. csv-table:: mat3 **(mats[0])** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "0.00", "0.00"
"row 2", "0.00", "1.00", "0.00"
"row 3", "0.00", "0.00", "1.00"
.. csv-table:: mat3 **(mats[1])** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "4.00", "13.00", "22.00"
"row 2", "5.00", "14.00", "23.00"
"row 3", "6.00", "15.00", "24.00"
.. csv-table:: mat3 **(mats[1])** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "0.00", "0.00"
"row 2", "0.00", "1.00", "0.00"
"row 3", "0.00", "0.00", "1.00"
.. csv-table:: mat3 **(mats[2])** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "7.00", "16.00", "25.00"
"row 2", "8.00", "17.00", "26.00"
"row 3", "9.00", "18.00", "27.00"
.. csv-table:: mat3 **(mats[2])** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "0.00", "0.00"
"row 2", "0.00", "1.00", "0.00"
"row 3", "0.00", "0.00", "1.00"
.. c:function:: void glm_mat3_zero(mat3 m)
Zero out the mat3 (m).
Parameters:
| *[in, out]* **m** mat3 (src, dest)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "0.00", "0.00", "0.00"
"row 2", "0.00", "0.00", "0.00"
"row 3", "0.00", "0.00", "0.00"
.. note:: Example
.. code-block:: c
mat3 m = {
{19.00,5.00,7.00},
{2.00,4.00,6.00},
{12.00,24.00,54.00},
};
glm_mat3_zero(m);
.. csv-table:: mat3 **(m)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "19.00", "2.00", "12.00"
"row 2", "5.00", "4.00", "24.00"
"row 3", "7.00", "6.00", "54.00"
.. csv-table:: mat3 **(m)** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "0.00", "0.00", "0.00"
"row 2", "0.00", "0.00", "0.00"
"row 3", "0.00", "0.00", "0.00"
.. c:function:: void glm_mat3_mul(mat3 m1, mat3 m2, mat3 dest)
Multiply mat3 (m1) by mat3 (m2) and store in mat3 (dest).
m1, m2 and dest matrices can be same matrix, it is possible to write this:
.. code-block:: c
mat3 m = GLM_MAT3_IDENTITY_INIT;
glm_mat3_mul(m, m, m);
Parameters:
| *[in]* **m1** mat3 (left)
| *[in]* **m2** mat3 (right)
| *[out]* **dest** destination (result, mat3)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(m1)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "a00", "a10", "a20"
"row 2", "a01", "a11", "a21"
"row 3", "a02", "a12", "a22"
.. csv-table:: mat3 **(m2)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "b00", "b10", "b20"
"row 2", "b01", "b11", "b21"
"row 3", "b02", "b12", "b22"
.. list-table:: mat3 **(dest)**
:header-rows: 1
* -
- column 1
- column 2
- column 3
* - row 1
- a00 * b00 + a10 * b01 + a20 * b02
- a00 * b10 + a10 * b11 + a20 * b12
- a00 * b20 + a10 * b21 + a20 * b22
* - row 2
- a01 * b00 + a11 * b01 + a21 * b02
- a01 * b10 + a11 * b11 + a21 * b12
- a01 * b20 + a11 * b21 + a21 * b22
* - row 3
- a02 * b00 + a12 * b01 + a22 * b02
- a02 * b10 + a12 * b11 + a22 * b12
- a02 * b20 + a12 * b21 + a22 * b22
.. note:: Example
.. code-block:: c
mat3 m = {
{19.00,5.00,6.00},
{2.00,4.00,8.00},
{1.00,3.00,7.00},
};
glm_mat3_mul(m, m, m);
.. csv-table:: mat3 **(m1)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "19.00", "2.00", "1.00"
"row 2", "5.00", "4.00", "3.00"
"row 3", "6.00", "8.00", "7.00"
.. csv-table:: mat3 **(m2)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "19.00", "2.00", "1.00"
"row 2", "5.00", "4.00", "3.00"
"row 3", "6.00", "8.00", "7.00"
.. list-table:: mat3 **(dest)**
:header-rows: 1
* -
- column 1
- column 2
- column 3
* - row 1
- **377.00** = 19.00 * 19.00 + 2.00 * 5.00 + 1.00 * 6.00
- **54.00** = 19.00 * 2.00 + 2.00 * 4.00 + 1.00 * 8.00
- **32.00** = 19.00 * 1.00 + 2.00 * 3.00 + 1.00 * 7.00
* - row 2
- **133.00** = 5.00 * 19.00 + 4.00 * 5.00 + 3.00 * 6.00
- **50.00** = 5.00 * 2.00 + 4.00 * 4.00 + 3.00 * 8.00
- **38.00** = 5.00 * 1.00 + 4.00 * 3.00 + 3.00 * 7.00
* - row 3
- **196.00** = 6.00 * 19.00 + 8.00 * 5.00 + 7.00 * 6.00
- **100.00** = 6.00 * 2.00 + 8.00 * 4.00 + 7.00 * 8.00
- **79.00** = 6.00 * 1.00 + 8.00 * 3.00 + 7.00 * 7.00
.. c:function:: void glm_mat3_mulv(mat3 m, vec3 v, vec3 dest)
Multiply mat3 (m) by vec3 (v) and store in vec3 (dest).
Parameters:
| *[in]* **m** mat3 (left)
| *[in]* **v** vec3 (right, column vector)
| *[out]* **dest** destination (result, column vector)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. csv-table:: column vec3 (1x3) **(v)**
:header: "", "column 1"
"row 1", "v0"
"row 2", "v1"
"row 3", "v2"
.. csv-table:: column vec3 (1x3) **(dest)**
:header: "", "column 1"
"row 1", "m00 * v0 + m10 * v1 + m20 * v2"
"row 2", "m01 * v0 + m11 * v1 + m21 * v2"
"row 3", "m02 * v0 + m12 * v1 + m22 * v2"
.. note:: Example
.. code-block:: c
vec3 dest;
vec3 v = {33.00,55.00,77.00};
mat3 m = {
{1.00,2.00,3.00},
{4.00,5.00,6.00},
{7.00,8.00,9.00},
};
glm_mat3_mulv(m, v, dest);
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "4.00", "7.00"
"row 2", "2.00", "5.00", "8.00"
"row 3", "3.00", "6.00", "9.00"
.. csv-table:: column vec3 **(v)**
:header: "", "column 1"
"row 1", "33.00"
"row 2", "55.00"
"row 3", "77.00"
.. csv-table:: vec2 **(dest)** Result
:header: "", "column 1"
"row 1", "**792.00** = 1.00 * 33.00 + 4.00 * 55.00 + 7.00 * 77.00"
"row 2", "**957.00** = 2.00 * 33.00 + 5.00 * 55.00 + 8.00 * 77.00"
"row 3", "**1122.00** = 3.00 * 33.00 + 6.00 * 55.00 + 9.00 * 77.00"
.. c:function:: void glm_mat3_transpose_to(mat3 mat, mat3 dest)
Transpose mat3 (mat) and store in mat3 (dest).
Parameters:
| *[in]* **mat** mat3 (left,src)
| *[out]* **dest** destination (result, mat3)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(mat)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. csv-table:: mat3 **(dest)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m01", "m02"
"row 2", "m10", "m11", "m12"
"row 3", "m20", "m21", "m22"
.. note:: Example
.. code-block:: c
mat3 mat = {
{1.00,2.00,3.00},
{4.00,5.00,6.00},
{7.00,8.00,9.00},
};
mat3 dest = GLM_MAT3_ZERO_INIT;
glm_mat3_transpose_to(mat, dest);
.. csv-table:: mat3 **(mat)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "4.00", "7.00"
"row 2", "2.00", "5.00", "8.00"
"row 3", "3.00", "6.00", "9.00"
.. csv-table:: mat3 **(dest)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "0.00", "0.00", "0.00"
"row 2", "0.00", "0.00", "0.00"
"row 3", "0.00", "0.00", "0.00"
.. csv-table:: mat3 **(dest)** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "2.00", "3.00"
"row 2", "4.00", "5.00", "6.00"
"row 2", "7.00", "8.00", "9.00"
.. c:function:: void glm_mat3_transpose(mat3 m)
Transpose mat3 (m) and store result in the same matrix.
Parameters:
| *[in, out]* **m** mat3 (src, dest)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(m)** src
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 2", "m02", "m12", "m22"
.. csv-table:: mat3 **(m)** dest
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m01", "m02"
"row 2", "m10", "m11", "m12"
"row 3", "m20", "m21", "m22"
.. note:: Example
.. code-block:: c
mat3 mat = {
{1.00,2.00,3.00},
{4.00,5.00,6.00},
{7.00,8.00,9.00},
};
glm_mat3_transpose(m);
.. csv-table:: mat3 **(m)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "4.00", "7.00"
"row 2", "2.00", "5.00", "8.00"
"row 3", "3.00", "6.00", "9.00"
.. csv-table:: mat3 **(m)** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "2.00", "3.00"
"row 2", "4.00", "5.00", "6.00"
"row 2", "7.00", "8.00", "9.00"
.. c:function:: void glm_mat3_scale(mat3 m, float s)
Multiply mat3 (m) by scalar constant (s).
Parameters:
| *[in, out]* **m** mat3 (src, dest)
| *[in]* **s** float (scalar)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00 * s", "m10 * s", "m20 * s"
"row 2", "m01 * s", "m11 * s", "m21 * s"
"row 3", "m02 * s", "m12 * s", "m22 * s"
.. note:: Example
.. code-block:: c
mat3 m = {
{1.00,2.00,3.00},
{4.00,5.00,6.00},
{7.00,8.00,9.00},
};
float s = 3.00f;
glm_mat3_scale(m, s);
.. csv-table:: mat3 **(m)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "1.00", "4.00", "7.00"
"row 2", "2.00", "5.00", "8.00"
"row 3", "3.00", "6.00", "9.00"
.. list-table:: mat3 **(m)** After
:header-rows: 1
* -
- column 1
- column 2
- column 3
* - row 1
- **3.00** = 1.00 * 3.00
- **12.00** = 4.00 * 3.00
- **21.00** = 7.00 * 3.00
* - row 2
- **6.00** = 2.00 * 3.00
- **15.00** = 5.00 * 3.00
- **24.00** = 8.00 * 3.00
* - row 3
- **9.00** = 3.00 * 3.00
- **18.00** = 6.00 * 3.00
- **27.00** = 9.00 * 3.00
.. c:function:: void glm_mat3_inv(mat3 mat, mat3 dest)
Inverse mat3 (mat) and store in mat3 (dest).
Parameters:
| *[in]* **mat** mat3 (left, src)
| *[out]* **dest** destination (result, inverse mat3)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(mat)**
:header: "", "column 1", "column 2", "column 3", "", ""
"row 1", "m00", "m10", "m20", "**m00**", "**m10**"
"row 2", "m01", "m11", "m21", "**m01**", "**m11**"
"row 3", "m02", "m12", "m22", "**m02**", "**m12**"
" ", "**m00**", "**m10**", "**m20**", "**m00**", "**m10**"
" ", "**m01**", "**m11**", "**m21**", "**m01**", "**m11**"
| For more information see `How to find the inverse of a 3 by 3 matrix (the fast way)[youtube]`_.
| Remember we are in column major not row major. So, the way the table is populated is slightly different.
| In terms of multiplication priority goes from m00,m01,m02,m11,...,m22.
| May utilize the distributive law to acquire bellow equations
.. math::
(m00 * m11 * m22) - (m00 * m21 * m12) = m00 * (m11 * m22 - m21 * m12)
.. list-table:: mat3 **(dest)**
:header-rows: 1
* -
- column 1
- column 2
- column 3
* - row 1
- | 1.0f / (
| m00 * (m11 * m22 - m12 * m21) -
| m01 * (m10 * m22 - m20 * m12) +
| m02 * (m10 * m21 - m20 * m11)
| ) * (m11 * m22 - m12 * m21)
- | -( 1.0f / (
| m00 * (m11 * m22 - m12 * m21) -
| m01 * (m10 * m22 - m20 * m12) +
| m02 * (m10 * m21 - m20 * m11)
| ) ) * (m10 * m22 - m20 * m12)
- | 1.0f / (
| m00 * (m11 * m22 - m12 * m21) -
| m01 * (m10 * m22 - m20 * m12) +
| m02 * (m10 * m21 - m20 * m11)
| ) * (m10 * m21 - m11 * m20)
* - row 2
- | -( 1.0f / (
| m00 * (m11 * m22 - m12 * m21) -
| m01 * (m10 * m22 - m20 * m12) +
| m02 * (m10 * m21 - m20 * m11)
| ) ) * (m01 * m22 - m21 * m02)
- | 1.0f / (
| m00 * (m11 * m22 - m12 * m21) -
| m01 * (m10 * m22 - m20 * m12) +
| m02 * (m10 * m21 - m20 * m11)
| ) * (m00 * m22 - m20 * m02)
- | -( 1.0f / (
| m00 * (m11 * m22 - m12 * m21) -
| m01 * (m10 * m22 - m20 * m12) +
| m02 * (m10 * m21 - m20 * m11)
| ) ) * (m00 * m21 - m20 * m01)
* - row 3
- | 1.0f / (
| m00 * (m11 * m22 - m12 * m21) -
| m01 * (m10 * m22 - m20 * m12) +
| m02 * (m10 * m21 - m20 * m11)
| ) * (m01 * m12 - m11 * m02)
- | -( 1.0f / (
| m00 * (m11 * m22 - m12 * m21) -
| m01 * (m10 * m22 - m20 * m12) +
| m02 * (m10 * m21 - m20 * m11)
| ) ) * (m00 * m12 - m10 * m02)
- | 1.0f / (
| m00 * (m11 * m22 - m12 * m21) -
| m01 * (m10 * m22 - m20 * m12) +
| m02 * (m10 * m21 - m20 * m11)
| ) * (m00 * m11 - m10 * m01)
.. note:: Example
.. code-block:: c
mat3 mat = {
{8.00,6.00,5.00},
{16.00,31.00,25.00},
{13.00,18.00,7.00},
};
mat3 dest = GLM_MAT3_ZERO_INIT;
glm_mat3_inv(mat, dest);
.. csv-table:: mat3 **(mat)** Before
:header: "", "column 1", "column 2", "column 3", "", ""
"row 1", "8.00", "16.00", "13.00", "**8.00**", "**16.00**"
"row 2", "6.00", "31.00", "18.00", "**6.00**", "**31.00**"
"row 3", "5.00", "25.00", "7.00", "**5.00**", "**25.00**"
" ", "**8.00**", "**16.00**", "**13.00**", "**8.00**", "**16.00**"
" ", "**6.00**", "**31.00**", "**18.00**", "**6.00**", "**31.00**"
.. list-table:: mat3 **(dest)** After
:header-rows: 1
* -
- column 1
- column 2
- column 3
* - row 1
- | **0.200** = 1.0 / (
| 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
| 6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
| 5.00 * (16.00 * 18.00 - 13.00 * 31.00)
| ) * (31.00 * 7.00 - 25.00 * 18.00)
- | **-0.184** = -( 1.0 / (
| 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
| 6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
| 5.00 * (16.00 * 18.00 - 13.00 * 31.00)
| ) ) * (16.00 * 7.00 - 13.00 * 25.00)
- | **0.099** = 1.0 / (
| 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
| 6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
| 5.00 * (16.00 * 18.00 - 13.00 * 31.00)
| ) * (16.00 * 18.00 - 31.00 * 13.00)
* - row 2
- | **-0.041** = -( 1.0 / (
| 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
| 6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
| 5.00 * (16.00 * 18.00 - 13.00 * 31.00)
| ) ) * (6.00 * 7.00 - 18.00 * 5.00)
- | **0.007** = 1.0 / (
| 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
| 6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
| 5.00 * (16.00 * 18.00 - 13.00 * 31.00)
| ) * (8.00 * 7.00 - 13.00 * 5.00)
- | **-0.056** = -( 1.0 / (
| 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
| 6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
| 5.00 * (16.00 * 18.00 - 13.00 * 31.00)
| ) ) * (8.00 * 18.00 - 13.00 * 6.00)
* - row 3
- | **0.004** = 1.0 / (
| 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
| 6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
| 5.00 * (16.00 * 18.00 - 13.00 * 31.00)
| ) * (6.00 * 25.00 - 31.00 * 5.00)
- | **0.103** = -( 1.0 / (
| 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
| 6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
| 5.00 * (16.00 * 18.00 - 13.00 * 31.00)
| ) ) * (8.00 * 25.00 - 16.00 * 5.00)
- | **-0.130** = 1.0 / (
| 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
| 6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
| 5.00 * (16.00 * 18.00 - 13.00 * 31.00)
| ) * (8.00 * 31.00 - 16.00 * 6.00)
.. c:function:: void glm_mat3_swap_col(mat3 mat, int col1, int col2)
Swap two columns in mat3 (mat) and store in same matrix.
Parameters:
| *[in, out]* **mat** mat3 (src, dest)
| *[in]* **col1** Column 1 array index
| *[in]* **col2** Column 2 array index
.. note:: Mathematical explanation
.. csv-table:: mat3 **(mat)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. code-block:: c
glm_mat3_swap_col(mat, 0, 1);
.. csv-table:: mat3 **(mat)** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "m10", "m00", "m20"
"row 2", "m11", "m01", "m21"
"row 3", "m12", "m02", "m22"
.. note:: Example
.. code-block:: c
mat3 mat = {
{8.00,6.00,5.00},
{16.00,31.00,25.00},
{13.00,18.00,7.00},
};
glm_mat3_swap_col(mat, 0, 1);
.. csv-table:: mat3 **(mat)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "8.00", "16.00", "13.00"
"row 2", "6.00", "31.00", "18.00"
"row 3", "5.00", "25.00", "7.00"
.. csv-table:: mat3 **(mat)** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "16.00", "8.00", "13.00"
"row 2", "31.00", "6.00", "18.00"
"row 3", "25.00", "5.00", "7.00"
.. c:function:: void glm_mat3_swap_row(mat3 mat, int row1, int row2)
Swap two rows in mat3 (mat) and store in same matrix.
Parameters:
| *[in, out]* **mat** mat3 (src, dest)
| *[in]* **row1** Row 1 array index
| *[in]* **row2** Row 2 array index
.. note:: Mathematical explanation
.. csv-table:: mat3 **(mat)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. code-block:: c
glm_mat3_swap_row(mat, 0, 1);
.. csv-table:: mat3 **(mat)** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "m01", "m11", "m21"
"row 2", "m00", "m10", "m20"
"row 3", "m02", "m12", "m22"
.. note:: Example
.. code-block:: c
mat3 mat = {
{8.00,6.00,5.00},
{16.00,31.00,25.00},
{13.00,18.00,7.00},
};
glm_mat3_swap_col(mat, 0, 1);
.. csv-table:: mat3 **(mat)** Before
:header: "", "column 1", "column 2", "column 3"
"row 1", "8.00", "16.00", "13.00"
"row 2", "6.00", "31.00", "18.00"
"row 3", "5.00", "25.00", "7.00"
.. csv-table:: mat3 **(mat)** After
:header: "", "column 1", "column 2", "column 3"
"row 1", "6.00", "31.00", "18.00"
"row 2", "8.00", "16.00", "13.00"
"row 3", "5.00", "25.00", "7.00"
.. c:function:: void glm_mat3_quat(mat3 m, versor dest)
convert mat3 to quaternion
Parameters:
| *[in]* **m** rotation matrix
| *[out]* **dest** destination quaternion
.. c:function:: void glm_mat3_textrans(float sx, float sy, float rot, float tx, float ty, mat3 dest)
Create texture transformation matrix, rotation is in radians CCW/RH
Parameters:
| *[in]* **sx** scale x
| *[in]* **sy** scale y
| *[in]* **rot** rotation in radians CCW/RH
| *[in]* **tx** translation x
| *[in]* **ty** translation y
| *[out]* **dest** destination matrix3x3
.. c:function:: float glm_mat3_det(mat3 m)
Returns mat3 determinant.
Parameters:
| *[in]* **m** mat3 (src)
Returns:
| mat3 determinant (float)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(mat)**
:header: "", "column 1", "column 2", "column 3", "", ""
"row 1", "m00", "m10", "m20", "**m00**", "**m10**"
"row 2", "m01", "m11", "m21", "**m01**", "**m11**"
"row 3", "m02", "m12", "m22", "**m02**", "**m12**"
" ", "**m00**", "**m10**", "**m20**", "**m00**", "**m10**"
" ", "**m01**", "**m11**", "**m21**", "**m01**", "**m11**"
| For more information see first portion of
| `How to find the inverse of a 3 by 3 matrix (the fast way)[youtube]`_.
.. code-block:: c
m00 * (m11 * m22 - m12 * m21) -
m01 * (m10 * m22 - m20 * m12) +
m02 * (m10 * m21 - m20 * m11)
.. note:: Example
.. code-block:: c
mat3 m = {
{8.00,6.00,5.00},
{16.00,31.00,25.00},
{13.00,18.00,7.00},
};
glm_mat3_det(m);
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3", "", ""
"row 1", "8.00", "16.00", "13.00", "**8.00**", "**16.00**"
"row 2", "6.00", "31.00", "18.00", "**6.00**", "**31.00**"
"row 3", "5.00", "25.00", "7.00", "**5.00**", "**25.00**"
.. code-block:: c
-1161.00 = 8.00 * (31.00 * 7.00 - 25.00 * 18.00) -
6.00 * (16.00 * 7.00 - 13.00 * 25.00) +
5.00 * (16.00 * 18.00 - 13.00 * 31.00)
.. c:function:: void glm_mat3_trace(mat3 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** mat3 (src)
Returns:
| mat3 trace (float)
.. note:: Mathematical explanation
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "m00", "m10", "m20"
"row 2", "m01", "m11", "m21"
"row 3", "m02", "m12", "m22"
.. code-block:: c
m00 + m11 + m22
.. note:: Example
.. code-block:: c
mat3 m = {
{8.00,6.00,5.00},
{16.00,31.00,25.00},
{13.00,18.00,7.00},
};
glm_mat3_trace(m);
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "8.00", "16.00", "13.00"
"row 2", "6.00", "31.00", "18.00"
"row 3", "5.00", "25.00", "7.00"
.. code-block:: c
82.00 = 8.00 + 31.00 + 7.00
.. c:function:: float glm_mat3_rmc(vec3 r, mat3 m, vec3 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 (3x1), ResC (1x3)) = scalar value.
Parameters:
| *[in]* **r** vec3 (3x1, row vector)
| *[in]* **m** mat3 (2x2, matrix)
| *[in]* **c** vec3 (1x3, column vector)
Returns:
| Scalar value (float, 1x1)
.. note:: Mathematical explanation
.. csv-table:: row vec3 (3x1) **(r)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "a00", "a10", "a20"
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "b00", "b10", "b20"
"row 2", "b01", "b11", "b21"
"row 3", "b02", "b12", "b22"
.. csv-table:: column vec3 (1x3) **(c)**
:header: "", "column 1"
"row 1", "c00"
"row 2", "c01"
"row 3", "c02"
.. code-block:: c
M * C = C (column vector)
dot_product(R, C)
.. csv-table:: column vec3 (1x3) **(C)**
:header: "", "column 1"
"row 1", "b00 * c00 + b10 * c01 + b20 * c02"
"row 2", "b01 * c00 + b11 * c01 + b21 * c02"
"row 3", "b02 * c00 + b11 * c01 + b22 * c02"
.. list-table:: float **(scalar)**
:header-rows: 1
* -
- column 1
* - row 1
- | a00 * (b00 * c00 + b10 * c01 + b20 * c02) +
| a10 * (b01 * c00 + b11 * c01 + b21 * c02) +
| a20 * (b02 * c00 + b11 * c01 + b22 * c02)
.. note:: Example
.. code-block:: c
vec3 r = {8.00,4.00,13.00};
vec3 c = {7.00,2.00,9.00};
mat3 m = {
{8.00,6.00,5.00},
{16.00,31.00,25.00},
{13.00,18.00,7.00},
};
glm_mat3_rmc(r, m, c);
.. csv-table:: row vec3 (3x1) **(r)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "8.00", "4.00", "13.00"
.. csv-table:: mat3 **(m)**
:header: "", "column 1", "column 2", "column 3"
"row 1", "8.00", "16.00", "13.00"
"row 2", "6.00", "31.00", "18.00"
"row 3", "5.00", "25.00", "7.00"
.. csv-table:: column vec3 (1x3) **(c)**
:header: "", "column 1"
"row 1", "7.00"
"row 2", "2.00"
"row 3", "9.00"
.. csv-table:: column vec3 (1x3) **(C)**
:header: "", "column 1"
"row 1", "**205.00** = 8.00 * 7.00 + 16.00 * 2.00 + 13.00 * 9.00"
"row 2", "**266.00** = 6.00 * 7.00 + 31.00 * 2.00 + 18.00 * 9.00"
"row 3", "**148.00** = 5.00 * 7.00 + 25.00 * 2.00 + 7.00 * 9.00"
.. csv-table:: float (1x1) **(scalar)**
:header: "", "column 1"
"row 1", "**4628.00** = 8.00 * 205.00 + 4.00 * 266.00 + 13.00 * 148.00"
.. _How to find the inverse of a 3 by 3 matrix (the fast way)[youtube]: https://www.youtube.com/watch?v=p8VnTCfJHAo
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