441 lines
10 KiB
Plaintext
441 lines
10 KiB
Plaintext
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Operations
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==========
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.. js:function:: add(a1, a2[, result])
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:param Matrix a1: first operand
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:param Matrix a2: second operand
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:param Matrix result: result buffer
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:returns: result
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Adds two buffers of the same size.
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.. js:function:: subtract(a1, a2[, result])
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:param Matrix a1: first operand
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:param Matrix a2: second operand
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:param Matrix result: result buffer
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:returns: result
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Subtracts two buffers of the same size.
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.. js:function:: scale(a, s[, result])
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:param Matrix a: buffer
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:param number s: scalar
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:param Matrix result: result
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:returns: result
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Scales a buffer by multiplying each component by a scalar.
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.. js:function:: equal(a1, a2[, e])
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:param Matrix a1: first operand
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:param Matrix a2: second operand
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:param number e: comparision tolerance, defaults to ``10E-5``
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:returns: true if operands are equal (within tolerance), false otherwise
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Compares two buffers component-wise for equality. Differences smaller than ``e`` are ignored.
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.. js:function:: clone(a[, result])
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:param Matrix a: buffer
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:param Matrix result: result buffer
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Creates a component-wise copy of a buffer.
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.. js:function:: clear(a[, s])
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:param Matrix a: buffer
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:param number s: scalar, defaults to 0
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Clears a buffer by writing a scalar into each component.
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.. js:function:: toMathML(a)
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:param Matrix a: buffer
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Converts a buffer to MathML representation.
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.. js:function:: toString(a)
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:param Matrix a: buffer
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Converts a buffer to string representation.
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Vector
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------
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.. js:function:: set(v, values)
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:param Vector v: vector
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:param Array values: array of values
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:returns: ``v``
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.. js:function:: length(v)
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:param Vector v: vector
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:returns: length of ``v``
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.. js:function:: length2(v)
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:param Vector v: vector
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:returns: squared length of ``v``
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.. js:function:: dot(v1, v2)
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:param Vector v1: first vector
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:param Vector v2: second vector
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:returns: inner product of ``v1`` and ``v2``
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.. js:function:: negate(v[, result])
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:param Vector v: vector
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:param Vector result: result
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:returns: negation of ``v``
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.. js:function:: limit(v, s[, result])
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:param Vector v: vector
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:param number s: scalar limit
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:returns: ``v`` resized to have length at most ``s``
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.. js:function:: normalize(v[, result])
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:param Vector v: vector
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:param Vector result: result
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:returns: a unit vector in the direction of ``v``
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.. js:function:: distance(v1, v2)
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:param Vector v1: origin vector
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:param Vector v2: target vector
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:returns: the distance from v1 to v2
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.. js:function:: angle(v1, v2)
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:param Vector v1: first vector
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:param Vector v2: second vector
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:returns: the angle betwen ``v1`` and ``v2``
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.. js:function:: lerp(v1, v2, s[, result])
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:param Vector v1: origin vector
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:param Vector v2: target vector
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:param number s: interpolation scalar
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:param Vector result: result
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:returns: interpolation from ``v1`` to ``v2`` by s
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.. js:function:: direction(v1, v2[, result])
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:param Vector v1: origin vector
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:param Vector v2: target vector
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:param Vector result: result
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:returns: unit vector pointing from ``v1`` to ``v2``
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.. js:function:: extract(v, offset, length[, result])
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:param Vector v: vector
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:param number offset: offset from the start ov ``v``
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:param number length: number of elements to extract
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:param Vector result: result
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:returns: ``length`` elements of ``v``, starting from ``offset``
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.. js:function:: zero(v)
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:param Vector v: vector
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:returns: ``v`` with all components 0
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.. js:function:: zero(d)
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:param number d: dimension
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:returns: a new ``Vector`` with all components 0
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.. js:function:: one(v)
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:param Vector v: vector
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:returns: ``v`` with all components 1
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.. js:function:: one(d)
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:param number d: dimension
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:returns: a new ``Vector`` with all components 1
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Vector2
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-------
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.. js:function:: x([result])
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:param Vector result: result
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:returns: 2-dimensional y unit vector (1, 0)
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.. js:function:: y([result])
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:param Vector result: result
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:returns: 2-dimensional y unit vector (0, 1)
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.. js:function:: u([result])
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:param Vector result: result
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:returns: 2-dimensional u unit vector (1, 0)
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.. js:function:: v([result])
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:param Vector result: result
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:returns: 2-dimensional v unit vector (0, 1)
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Vector3
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-------
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.. js:function:: cross(v1, v2[, result])
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:param Vector v1: first vector
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:param Vector v2: second vector
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:param Vector result: result
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:returns: outer product of ``v1`` and ``v2``
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.. js:function:: unproject(v, view, projection, viewport[, result])
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.. note:: Not yet implemented
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:param Vector v: screen space vector
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:param Matrix view: view matrix
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:param Matrix projection: projection matrix
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:param Array viewport: viewport parameters, as ``[x, y, width, height]``
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:param Vector result: result
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:returns: vector projected from screen space to object space
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.. js:function:: x([result])
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:param Vector result: result
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:returns: 3-dimensional y unit vector (1, 0, 0)
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.. js:function:: y([result])
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:param Vector result: result
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:returns: 3-dimensional y unit vector (0, 1, 0)
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.. js:function:: z([result])
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:param Vector result: result
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:returns: 3-dimensional z unit vector (0, 0, 1)
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Vector4
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--------
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.. js:function:: x([result])
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:param Vector result: result
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:returns: 4-dimensional y unit vector (1, 0, 0, 0)
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.. js:function:: y([result])
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:param Vector result: result
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:returns: 4-dimensional y unit vector (0, 1, 0, 0)
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.. js:function:: z([result])
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:param Vector result: result
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:returns: 4-dimensional z unit vector (0, 0, 1, 0)
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.. js:function:: w([result])
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:param Vector result: result
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:returns: 4-dimensional w unit vector (0, 0, 0, 1)
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Quaternion
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----------
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.. js:function:: inverse(q[, result])
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:param Quaternion q: quaternion
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:param Quaternion result: result
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:returns: inverse of ``q``
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.. js:function:: conjugate(q[, result])
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:param Quaternion q: quaternion
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:param Quaternion result: result
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:returns: conjugate of ``q``
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.. js:function:: identity([result])
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:param Quaternion result: result
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:returns: the identity quaternion (0, 0, 0, 1)
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.. js:function:: slerp(q1, q2, s[, result])
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:param Quaternion q1: origin quaternion
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:param Quaternion q2: target quaternion
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:param number s: interpolation scalar
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:param Quaternion result: result
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:returns: spherical linear interpolation between ``q1`` and ``q2``
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.. js:function:: rotation(v1, v2[, result])
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.. note:: Not yet implemented
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:param Vector v1: origin vector
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:param Vector v2: target vector
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:param Quaternion result: result
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:returns: quaternion of rotation between two 3-dimensional vectors
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.. js:function:: toAxisAngle(q[, result])
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:param Quaternion q: quaternion
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:param Vector result: result
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:returns: axis-angle representated as a 3-dimensional vector
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.. js:function:: fromAxisAngle(v[, result])
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:param Vector v: vector
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:param Quaternion result: result
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:returns: quaternion computed from axis-angle as a 3-dimensional vector
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Matrix
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------
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.. js:function:: multiply(m1, m2[, reuslt])
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:param Matrix m1: first matrix
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:param Matrix m2: second matrix
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:param Matrix result: result
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:returns: the matrix product of ``m1`` with ``m2``
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.. js:function:: inverse(m[, result])
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.. note:: Valid for square matrices only
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:param Matrix m: square matrix
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:param Matrix result: result
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:returns: inverse of ``m``
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.. js:function:: transpose(m[, result])
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.. note:: Implemented for square matrices only
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:param Matrix m: matrix
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:param Matrix result: result
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:returns: transpose of ``m``
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.. js:function:: identity(m)
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.. note:: Valid for square matrices only
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:param Matrix m: square matrix
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:returns: identity matrix
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.. js:function:: identity(d)
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:param number d: dimension
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:returns: identity matrix of dimension ``d``
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.. js:function:: extract(m, rowOffset, columnOffset, rows, columns[, result])
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.. note:: Not yet implemented
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:param Matrix m: matrix
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:param number rowOffset: starting row
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:param number columnOffset: starting column
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:param number rows: number of rows to extract
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:param number columns: number of columns to extract
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:param Matrix result: result
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:returns: sub-matrix of ``m``
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Matrix2
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-------
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.. js:function:: toAngle(m)
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:param Matrix m: rotation matrix
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:returns: angle in radians
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.. js:function:: fromAngle(angle[, result])
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:param number angle: angle in radians
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:param Matrix result: result
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:returns: 2-dimensional rotation matrix
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Matrix3
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-------
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.. js:function:: toQuaternion(m[, result])
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.. note:: Not yet implemented
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:param Matrix m: rotation matrix
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:param Quaternion result: result
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:returns: quaternion rotation
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.. js:function:: fromQuaternion(q[, result])
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.. note:: Not yet implemented
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:param Quaternion q: quaternion
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:param Matrix result: matrix
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:returns: rotation matrix
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.. js:function:: toAxisAngle(m[, result])
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.. note:: Not yet implemented
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:param Matrix m: matrix
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:param Vector result: vector
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:returns: axis-angle vector
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.. js:function:: fromAxisAngle(v[, result])
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.. note:: Not yet implemented
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:param Vector v: axis-angle vector
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:param Matrix result: result
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:returns: rotation matrix
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Transform
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---------
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.. js:function:: translate(left, right[, result])
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.. note:: One of the operands must be a Transform
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:param left: left operand
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:param right: right operand
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:param Transform result: result
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:returns: transform with translation applied
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The translation should be expressed as a 3-dimensional vector.
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.. js:function:: rotate(left, right[, result])
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.. note:: One of the operands must be a Transform
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:param left: left operand
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:param right: right operand
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:param Transform result: result
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:returns: transform with rotation applied
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The rotation should be expressed as an angle or rotation matrix for 2 dimensions, or rotation matrix, axis-angle or quaternion for 3 dimensions.
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.. js:function:: scale(left, right[, result])
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.. note:: One of the operands must be a Transform
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:param left: left operand
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:param right: right operand
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:param Transform result: result
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:returns: transform with scaling applied
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The scaling should be expressed as a vector, with each component specifying the factor in the corresponding dimension.
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.. js:function:: linear(t[, result])
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:param Transform t: transform
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:param Matrix result: result
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:returns: linear part (rotation and scaling) of the affine transform
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.. js:function:: svd(t, translation, rotation, scaling)
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:param Transform t: transform
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:param Vector translation: result vector to store translation
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:param Quaternion rotation: result quaternion to store rotation
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:param Vector scaling: result vector to store scaling
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