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