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Content import math class Matrix: """ Represents a mathematical matrix or vector. It is possible to fill this with anything one can multiply or add, even more matrices. """ width = 0 height = 0 entries = [] def multiply(self, other): # Explicit multiply """Explicit version of the multiply operator.""" if type(other) == int or type(other) == float: # By number out = [[0] * self.height for i in range(self.width)] for y in range(0, self.height): for x in range(0, self.width): out[x][y] = self.entries[x][y] * other return self.__matrix_implicit(self.width, self.height, out) elif other.width == 1: # By vector if other.height != self.width: raise Exception("Illegal matrix-vector multiplication: other vector size ({}) " "must match this matrix width ({})".format(other.height, self.width)) out = [[0] * self.width] for y in range(0, self.height): for x in range(0, self.width): out[0][y] += self.entries[x][y] * other.entries[0][x] return self.__matrix_implicit(1, self.height, out) else: # By matrix if other.height != self.width: raise Exception("Illegal matrix multiplication: other matrix height ({}) " "must match this matrix width ({})".format(other.height, self.width)) out = [[0] * self.height for i in range(other.width)] for leftX in range(self.width): for leftY in range(self.height): for col in range(other.width): out[col][leftY] += self.entries[leftX][leftY] * other.entries[col][leftX] return self.__matrix_implicit(other.width, self.height, out) def __mul__(self, other): # Implicit multiply return self.multiply(other) def add(self, other): """Explicit version of the add operator.""" if type(other) != Matrix: # Add non-matrix new = matrix_copy(self) for y in range(0, self.height): for x in range(0, self.width): new.entries[x][y] += other return new else: # Add matrix if other.width != self.width or other.height != self.height: raise Exception("Illegal matrix addition: other matrix ({}, {}) must be the same size as " "this matrix ({}, {})".format(other.width, other.height, self.width, self.height)) new = matrix_copy(self) for y in range(0, self.height): for x in range(0, self.width): new.entries[x][y] += other.entries[x][y] return new def __add__(self, other): return self.add(other) def __str__(self): maxW = 0 for x in range(0, self.width): for y in range(0, self.height): w = len(str(self.entries[x][y])) if w > maxW: maxW = w ret = "" for y in range(0, self.height): ret += "[ " for x in range(0, self.width): stuff = str(self.entries[x][y]) ret += stuff + " " * (maxW + 1 - len(stuff)) ret += "]\r\n" return ret def __matrix_implicit(self, width: int, height: int, entries: list): # Implicit constructor """Makes a matrix directly from its components, does not copy entries.""" mtx = Matrix() mtx.width = width mtx.height = height mtx.entries = entries return mtx def vector(*content): """Makes a vector with the given contents.""" self = Matrix() self.width = 1 self.height = len(content) self.entries = [[0] * self.height] for i in range(0, len(content)): self.entries[0][i] = content[i] return self def vector_empty(size): """Makes an empty vector of the given size.""" self = Matrix() self.width = 1 self.height = size self.entries = [[0] * self.height] return self def matrix_empty(width, height): """Makes an empty matrix of the given size.""" self = Matrix() self.width = width self.height = height self.entries = [[0] * self.height for i in range(self.width)] return self def matrix_copy(other): # Copy constructor """Makes a copy of a matrix.""" self = Matrix() self.width = other.width self.height = other.height self.entries = [[0] * self.height for i in range(self.width)] for y in range(0, self.height): for x in range(0, self.width): self.entries[x][y] = other.entries[x][y] return self def matrix_identity(size: int): # Identity "constructor" """Makes an identity matrix of given dimensions.""" mtx = Matrix() mtx.width = size mtx.height = size mtx.entries = [[0] * size for i in range(size)] # Create array for i in range(0, size): mtx.entries[i][i] = 1 # Add identity return mtx def matrix_implicit(width, height, entries): """Makes making a matrix alot easier.""" self = matrix_empty(width, height) for y in range(0, height): for x in range(0, width): self.entries[x][y] = entries[y * width + x] return self def matrix_rotate_2D(angle): """Makes a matrix representing a 2D rotation.""" return matrix_implicit(3, 3, [ math.cos(angle), -math.sin(angle), 0, math.sin(angle), math.cos(angle), 0, 0, 0, 1 ]) def matrix_translate_2D(x, y): """Makes a matrix representing a 2D move.""" return matrix_implicit(3, 3, [ 1, 0, x, 0, 1, y, 0, 0, 1 ]) def matrix_scale_uniform_2D(factor): """Makes a matrix representing a uniform 2D scaling.""" return matrix_implicit(3, 3, [ factor, 0, 0, 0, factor, 0, 0, 0, 1 ]) def matrix_scale_2D(scaleX, scaleY): """Makes a matrix representing a 2D scaling.""" return matrix_implicit(3, 3, [ scaleY, 0, 0, 0, scaleX, 0, 0, 0, 1 ]) class MatrixStack2D: """Matrix stack which can represent simple 2D transformations such as scaling, rotating and moving.""" matrices = [] currentMatrix = None def __init__(self): self.clear() # Not really much more to do def multiplyMatrix(self, value): """ Multiplies by a given input matrix. The input must be either 3 by 3 or 2 rows by 3 columns. If the input if 2x3, it will be converted internally. """ if value.height == 2: value = matrix_implicit(3, 3, [ value.entries[0][0], value.entries[1][0], value.entries[2][0], value.entries[0][1], value.entries[1][1], value.entries[2][1], 0, 0, 1 ]) self.currentMatrix *= value def clear(self): self.currentMatrix = matrix_identity(3) # Identity matrix self.matrices = [] # Empty stack def push(self): """Pushes the current matrix onto the stack, thereby preserving it for later use.""" self.matrices.append(matrix_copy(self.currentMatrix)) def pop(self): """Pops a matrix off of the matrix stack and sets the current matrix.""" if len(self.matrices) == 0: raise Exception("Matrix stack is already empty!") self.currentMatrix = matrix_copy(self.matrices[len(self.matrices) - 1]) self.matrices.pop() def transformPoint(self, x, y): """Transforms the given point by the current transformation.""" point = self.currentMatrix * vector(x, y, 1) return point.entries[0][0], point.entries[0][1] def translate(self, x, y): """Applies a transformation equivalent to moving relatively by X, Y.""" self.currentMatrix *= matrix_translate_2D(x, y) def rotate2D(self, angleRadians): """Applies a transformation equivalent to rotating the entire canvas in 2D.""" self.currentMatrix *= matrix_rotate_2D(angleRadians) def scale2D(self, scaleX, scaleY): """Applies a transformation equivalent to scaling X and Y in 2D.""" self.currentMatrix *= matrix_scale_2D(scaleX, scaleY)