Difficult-Rocket/bin/libs/pyglet/math.py

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"""Matrix and Vector operations.

This module provides classes for Matrix and Vector math.
A :py:class:`~pyglet.matrix.Mat4` class is available for representing
4x4 matricies, including helper methods for rotating, scaling, and
transforming. The internal datatype of :py:class:`~pyglet.matrix.Mat4`
is a 1-dimensional array, so instances can be passed directly to OpenGL.

"""

import math as _math
import operator as _operator
import warnings as _warnings


def create_orthogonal(left, right, bottom, top, znear, zfar):
    """Create a Mat4 orthographic projection matrix."""
    width = right - left
    height = top - bottom
    depth = zfar - znear

    sx = 2.0 / width
    sy = 2.0 / height
    sz = 2.0 / -depth

    tx = -(right + left) / width
    ty = -(top + bottom) / height
    tz = -(zfar + znear) / depth

    return Mat4((sx, 0.0, 0.0, 0.0,
                 0.0, sy, 0.0, 0.0,
                 0.0, 0.0, sz, 0.0,
                 tx, ty, tz, 1.0))


def create_perspective(left, right, bottom, top, znear, zfar, fov=60):
    """Create a Mat4 perspective projection matrix."""
    width = right - left
    height = top - bottom
    aspect = width / height

    xymax = znear * _math.tan(fov * _math.pi / 360)
    ymin = -xymax
    xmin = -xymax

    width = xymax - xmin
    height = xymax - ymin
    depth = zfar - znear
    q = -(zfar + znear) / depth
    qn = -2 * zfar * znear / depth

    w = 2 * znear / width
    w = w / aspect
    h = 2 * znear / height

    return Mat4((w, 0, 0, 0,
                 0, h, 0, 0,
                 0, 0, q, -1,
                 0, 0, qn, 0))


class Mat4(tuple):
    """A 4x4 Matrix

    `Mat4` is a simple immutable 4x4 Matrix, with a few operators.
    Two types of multiplication are possible. The "*" operator
    will perform elementwise multiplication, wheras the "@"
    operator will perform Matrix multiplication. Internally,
    data is stored in a linear 1D array, allowing direct passing
    to OpenGL.
    """

    def __new__(cls, values=None):
        """Create a 4x4 Matrix

        A Matrix can be created with a list or tuple of 16 values.
        If no values are provided, an "identity matrix" will be created
        (1.0 on the main diagonal). Matrix objects are immutable, so
        all operations return a new Mat4 object.

        :Parameters:
            `values` : tuple of float or int
                A tuple or list containing 16 floats or ints.
        """
        assert values is None or len(values) == 16, "A 4x4 Matrix requires 16 values"
        return super().__new__(Mat4, values or (1.0, 0.0, 0.0, 0.0,
                                                0.0, 1.0, 0.0, 0.0,
                                                0.0, 0.0, 1.0, 0.0,
                                                0.0, 0.0, 0.0, 1.0))

    def row(self, index):
        """Get a specific row as a tuple."""
        return self[index*4:index*4+4]

    def column(self, index):
        """Get a specific column as a tuple."""
        return self[index::4]

    def scale(self, x=1, y=1, z=1):
        """Get a scale Matrix on x, y, or z axis."""
        temp = list(self)
        temp[0] *= x
        temp[5] *= y
        temp[10] *= z
        return Mat4(temp)

    def translate(self, x=0, y=0, z=0):
        """Get a translate Matrix along x, y, and z axis."""
        return Mat4(self) @ Mat4((1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1))

    def rotate(self, angle=0, x=0, y=0, z=0):
        """Get a rotation Matrix on x, y, or z axis."""
        assert all(abs(n) <= 1 for n in (x, y, z)), "x,y,z must be normalized (<=1)"
        c = _math.cos(angle)
        s = _math.sin(angle)
        t = 1 - c
        tempx, tempy, tempz = t * x, t * y, t * z

        ra = c + tempx * x
        rb = 0 + tempx * y + s * z
        rc = 0 + tempx * z - s * y
        re = 0 + tempy * x - s * z
        rf = c + tempy * y
        rg = 0 + tempy * z + s * x
        ri = 0 + tempz * x + s * y
        rj = 0 + tempz * y - s * x
        rk = c + tempz * z

        # ra, rb, rc, --
        # re, rf, rg, --
        # ri, rj, rk, --
        # --, --, --, --

        return Mat4(self) @ Mat4((ra, rb, rc, 0, re, rf, rg, 0, ri, rj, rk, 0, 0, 0, 0, 1))

    def transpose(self):
        """Get a tranpose of this Matrix."""
        return Mat4(self[0::4] + self[1::4] + self[2::4] + self[3::4])

    def __add__(self, other):
        assert len(other) == 16, "Can only add to other Mat4 types"
        return Mat4(tuple(s + o for s, o in zip(self, other)))

    def __sub__(self, other):
        assert len(other) == 16, "Can only subtract from other Mat4 types"
        return Mat4(tuple(s - o for s, o in zip(self, other)))

    def __pos__(self):
        return self

    def __neg__(self):
        return Mat4(tuple(-v for v in self))

    def __invert__(self):
        a = self[10] * self[15] - self[11] * self[14]
        b = self[9] * self[15] - self[11] * self[13]
        c = self[9] * self[14] - self[10] * self[13]
        d = self[8] * self[15] - self[11] * self[12]
        e = self[8] * self[14] - self[10] * self[12]
        f = self[8] * self[13] - self[9] * self[12]
        g = self[6] * self[15] - self[7] * self[14]
        h = self[5] * self[15] - self[7] * self[13]
        i = self[5] * self[14] - self[6] * self[13]
        j = self[6] * self[11] - self[7] * self[10]
        k = self[5] * self[11] - self[7] * self[9]
        l = self[5] * self[10] - self[6] * self[9]
        m = self[4] * self[15] - self[7] * self[12]
        n = self[4] * self[14] - self[6] * self[12]
        o = self[4] * self[11] - self[7] * self[8]
        p = self[4] * self[10] - self[6] * self[8]
        q = self[4] * self[13] - self[5] * self[12]
        r = self[4] * self[9] - self[5] * self[8]

        det = (self[0] * (self[5] * a - self[6] * b + self[7] * c)
               - self[1] * (self[4] * a - self[6] * d + self[7] * e)
               + self[2] * (self[4] * b - self[5] * d + self[7] * f)
               - self[3] * (self[4] * c - self[5] * e + self[6] * f))

        if det == 0:
            _warnings.warn("Unable to calculate inverse of singular Matrix")
            return self

        pdet = 1 / det
        ndet = -pdet

        return Mat4((pdet * (self[5] * a - self[6] * b + self[7] * c),
                     ndet * (self[1] * a - self[2] * b + self[3] * c),
                     pdet * (self[1] * g - self[2] * h + self[3] * i),
                     ndet * (self[1] * j - self[2] * k + self[3] * l),
                     ndet * (self[4] * a - self[6] * d + self[7] * e),
                     pdet * (self[0] * a - self[2] * d + self[3] * e),
                     ndet * (self[0] * g - self[2] * m + self[3] * n),
                     pdet * (self[0] * j - self[2] * o + self[3] * p),
                     pdet * (self[4] * b - self[5] * d + self[7] * f),
                     ndet * (self[0] * b - self[1] * d + self[3] * f),
                     pdet * (self[0] * h - self[1] * m + self[3] * q),
                     ndet * (self[0] * k - self[1] * o + self[3] * r),
                     ndet * (self[4] * c - self[5] * e + self[6] * f),
                     pdet * (self[0] * c - self[1] * e + self[2] * f),
                     ndet * (self[0] * i - self[1] * n + self[2] * q),
                     pdet * (self[0] * l - self[1] * p + self[2] * r)))

    def __round__(self, n=None):
        return Mat4(tuple(round(v, n) for v in self))

    def __mul__(self, other):
        raise NotImplementedError("Please use the @ operator for Matrix multiplication.")

    def __matmul__(self, other):
        assert len(other) == 16, "Can only multiply with other Mat4 types"
        # Rows:
        r0 = self[0:4]
        r1 = self[4:8]
        r2 = self[8:12]
        r3 = self[12:16]
        # Columns:
        c0 = other[0::4]
        c1 = other[1::4]
        c2 = other[2::4]
        c3 = other[3::4]

        # Multiply and sum rows * colums:
        return Mat4((sum(map(_operator.mul, r0, c0)),
                     sum(map(_operator.mul, r0, c1)),
                     sum(map(_operator.mul, r0, c2)),
                     sum(map(_operator.mul, r0, c3)),

                     sum(map(_operator.mul, r1, c0)),
                     sum(map(_operator.mul, r1, c1)),
                     sum(map(_operator.mul, r1, c2)),
                     sum(map(_operator.mul, r1, c3)),

                     sum(map(_operator.mul, r2, c0)),
                     sum(map(_operator.mul, r2, c1)),
                     sum(map(_operator.mul, r2, c2)),
                     sum(map(_operator.mul, r2, c3)),

                     sum(map(_operator.mul, r3, c0)),
                     sum(map(_operator.mul, r3, c1)),
                     sum(map(_operator.mul, r3, c2)),
                     sum(map(_operator.mul, r3, c3))))

    def __repr__(self):
        return f"{self.__class__.__name__}{self[0:4]}\n    {self[4:8]}\n    {self[8:12]}\n    {self[12:16]}"