update docs

docs/source/api.rst

@@ -47,3 +47,4 @@ Follow the :doc:`build` documentation for this
    call
    sphere
    curve
+   bezier

docs/source/bezier.rst

@@ -0,0 +1,89 @@
+.. default-domain:: C
+
+Bezier
+================================================================================
+
+Header: cglm/bezier.h
+
+Common helpers for cubic bezier and similar curves.
+
+Table of contents (click to go):
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Functions:
+
+1. :c:func:`glm_bezier`
+2. :c:func:`glm_hermite`
+3. :c:func:`glm_decasteljau`
+
+Functions documentation
+~~~~~~~~~~~~~~~~~~~~~~~
+
+.. c:function:: float glm_bezier(float s, float p0, float c0, float c1, float p1)
+
+    | cubic bezier interpolation
+    | formula:
+
+    .. code-block:: text
+
+      B(s) = P0*(1-s)^3 + 3*C0*s*(1-s)^2 + 3*C1*s^2*(1-s) + P1*s^3
+
+    | similar result using matrix:
+
+    .. code-block:: text
+
+      B(s) = glm_smc(t, GLM_BEZIER_MAT, (vec4){p0, c0, c1, p1})
+
+    | glm_eq(glm_smc(...), glm_bezier(...)) should return TRUE
+
+    Parameters:
+      | *[in]*  **s**   parameter between 0 and 1
+      | *[in]*  **p0**  begin point
+      | *[in]*  **c0**  control point 1
+      | *[in]*  **c1**  control point 2
+      | *[in]*  **p1**  end point
+
+    Returns:
+        B(s)
+
+.. c:function:: float glm_hermite(float s, float p0, float t0, float t1, float p1)
+
+    | cubic hermite interpolation
+    | formula:
+
+    .. code-block:: text
+
+      H(s) = P0*(2*s^3 - 3*s^2 + 1) + T0*(s^3 - 2*s^2 + s) + P1*(-2*s^3 + 3*s^2) + T1*(s^3 - s^2)
+
+    | similar result using matrix:
+
+    .. code-block:: text
+
+      H(s) = glm_smc(t, GLM_HERMITE_MAT, (vec4){p0, p1, c0, c1})
+
+    | glm_eq(glm_smc(...), glm_hermite(...)) should return TRUE
+
+
+    Parameters:
+      | *[in]*  **s**   parameter between 0 and 1
+      | *[in]*  **p0**  begin point
+      | *[in]*  **t0**  tangent 1
+      | *[in]*  **t1**  tangent 2
+      | *[in]*  **p1**  end point
+
+    Returns:
+        B(s)
+
+.. c:function:: float glm_decasteljau(float prm, float p0, float c0, float c1, float p1)
+
+    | iterative way to solve cubic equation
+
+    Parameters:
+      | *[in]*  **prm** parameter between 0 and 1
+      | *[in]*  **p0**  begin point
+      | *[in]*  **c0**  control point 1
+      | *[in]*  **c1**  control point 2
+      | *[in]*  **p1**  end point
+
+    Returns:
+        parameter to use in cubic equation