Pygame 围绕轴旋转立方体

问题描述

我一直在玩旋转立方体的例子

最小示例:

导入数学导入pygamedef 项目(向量，w，h，fov，距离):因子 = math.atan(fov/2 * math.pi/180)/(距离 + vector.z)x = 矢量.x * 因子 * w + w/2y = -vector.y * 因子 * w + h/2返回 pygame.math.Vector3(x, y, vector.z)def rotate_vertices(顶点，角度，轴):return [v.rotate(angle, axis) for v in vertices]def scale_vertices(顶点，s):返回 [pygame.math.Vector3(v[0]*s[0], v[1]*s[1], v[2]*s[2]) for v in vertices]def translate_vertices(顶点，t):return [v + pygame.math.Vector3(t) for v in vertices]def project_vertices(顶点，w，h，fov，距离):return [project(v, w, h, fov, distance) for v in vertices]类网格():def __init__(自我，顶点，面):self.__vertices = [pygame.math.Vector3(v) for v in vertices]self.__faces = 面孔def旋转(自我，角度，轴):self.__vertices = rotate_vertices(self.__vertices, 角度, 轴)def 比例(自我，s):self.__vertices = scale_vertices(self.__vertices, s)定义翻译(自我，t):self.__vertices = translate_vertices(self.__vertices, t)def calculate_average_z(自我，顶点):return [(i, sum([vertices[j].z for j in f])/len(f)) for i, f in enumerate(self.__faces)]def get_face(自我，索引):返回 self.__faces[index]def get_vertices(self):返回自我.__顶点def create_polygon(self, face, vertices):返回 [(vertices[i].x, vertices[i].y) for i in [*face, face[0]]]课堂场景:def __init__(self, mehses, fov, distance):self.meshes = mehsesself.fov = fovself.distance = 距离self.euler_angles = [0, 0, 0]def transform_vertices(自我，顶点，宽度，高度):转换的_vertices = 顶点axis_list = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]对于角度，轴反转(list(zip(list(self.euler_angles)，axis_list))):变换顶点 = 旋转顶点(变换顶点，角度，轴)转换顶点 = 项目顶点(转换顶点，宽度，高度，self.fov，self.distance)返回transformed_verticesdef 绘制(自我，表面):多边形 = []对于 self.meshes 中的网格:transform_vertices = self.transform_vertices(mesh.get_vertices(), *surface.get_size())avg_z = mesh.calculate_average_z(transformed_vertices)对于 avg_z 中的 z:#for z in sorted(avg_z, key=lambda x: x[1], reverse=True):点列表 = mesh.create_polygon(mesh.get_face(z[0])，transformed_vertices)多边形.附加((点列表，z [1]))#pygame.draw.polygon(surface, (128, 128, 192), pointlist)#pygame.draw.polygon(surface, (0, 0, 0), pointlist, 3)对于排序中的多边形(多边形，键= lambda x:x [1]，反向=真):pygame.draw.polygon(表面, (128, 128, 192), poly[0])pygame.draw.polygon(surface, (0, 0, 0), poly[0], 3)顶点 = [(-1,-1,1), (1,-1,1), (1,1,1), (-1,1,1), (-1,-1,-1),(1,-1,-1), (1,1,-1), (-1,1,-1)]面 = [(0,1,2,3), (1,5,6,2), (5,4,7,6), (4,0,3,7), (3,2,6,7), (1,0,4,5)]cube_origins = [(-1, -1, 0), (0, -1, 0), (1, -1, 0), (1, 0, 0), (1, 1, 0), (0,1, 0), (-1, 1, 0), (-1, 0, 0)]网格 = []对于 cube_origins 中的原点:立方体=网格(顶点，面)立方体.scale((0.5, 0.5, 0.5))cube.translate(原点)网格.附加(立方体)场景 = 场景(网格，90, 5)pygame.init()窗口 = pygame.display.set_mode((400, 300))时钟 = pygame.time.Clock()运行=真运行时:时钟.tick(60)对于 pygame.event.get() 中的事件:如果 event.type == pygame.QUIT:运行 = 假window.fill((255, 255, 255))场景.draw(窗口)场景.euler_angles[1] += 1pygame.display.flip()pygame.quit()

I have been playing around with the example of a rotating cube here. I have generated 2 cubes that should rotate around the Y-axis. However, it doesn't seem to work as expected and I can't figure out what the problem of it is.

Here is a working code example:

import sys
import math
import pygame

from pygame.math import Vector3
from enum import Enum


class Color(Enum):
    BLACK = (0, 0, 0)
    SILVER = (192,192,192)


class Cube():

    def __init__(self, vectors, screen_width, screen_height, initial_angle=25):
        self._vectors = vectors
        self._angle = initial_angle
        self._screen_width = screen_width
        self._screen_height = screen_height

        # Define the vectors that compose each of the 6 faces
        self._faces  = [(0,1,2,3),
                       (1,5,6,2),
                       (5,4,7,6),
                       (4,0,3,7),
                       (0,4,5,1),
                       (3,2,6,7)]

        self._setup_initial_positions(initial_angle)

    def _setup_initial_positions(self, angle):
        tmp = []
        for vector in self._vectors:
            rotated_vector = vector.rotate_x(angle).rotate_y(angle)#.rotateZ(self.angle)
            tmp.append(rotated_vector)

        self._vectors = tmp

    def transform_vectors(self, new_angle):
        # It will hold transformed vectors.
        transformed_vectors = []

        for vector in self._vectors:
            # Rotate the point around X axis, then around Y axis, and finally around Z axis.
            mod_vector = vector.rotate_y(new_angle)
            # Transform the point from 3D to 2D
            mod_vector = self._project(mod_vector, self._screen_width, self._screen_height, 256, 4)
            # Put the point in the list of transformed vectors
            transformed_vectors.append(mod_vector)

        return transformed_vectors

    def _project(self, vector, win_width, win_height, fov, viewer_distance):
        factor = fov / (viewer_distance + vector.z)
        x = vector.x * factor + win_width / 2
        y = -vector.y * factor + win_height / 2
        return Vector3(x, y, vector.z)

    def calculate_average_z(self, vectors):
        avg_z = []
        for i, face in enumerate(self._faces):
            # for each point of a face calculate the average z value
            z = (vectors[face[0]].z + 
                 vectors[face[1]].z + 
                 vectors[face[2]].z + 
                 vectors[face[3]].z) / 4.0
            avg_z.append([i, z])

        return avg_z

    def get_face(self, index):
        return self._faces[index]

    def create_polygon(self, face, transformed_vectors):
        return [(transformed_vectors[face[0]].x, transformed_vectors[face[0]].y), 
                (transformed_vectors[face[1]].x, transformed_vectors[face[1]].y),
                (transformed_vectors[face[2]].x, transformed_vectors[face[2]].y),
                (transformed_vectors[face[3]].x, transformed_vectors[face[3]].y),
                (transformed_vectors[face[0]].x, transformed_vectors[face[0]].y)]


class Simulation:
    def __init__(self, win_width=640, win_height=480):
        pygame.init()

        self.screen = pygame.display.set_mode((win_width, win_height))

        self.clock = pygame.time.Clock()

        cube = Cube([
            Vector3(0, 0.5, -0.5),
            Vector3(0.5, 0.5, -0.5),
            Vector3(0.5, 0, -0.5),
            Vector3(0, 0, -0.5),
            Vector3(0, 0.5, 0),
            Vector3(0.5, 0.5, 0),
            Vector3(0.5, 0, 0),
            Vector3(0, 0, 0)
        ], win_width, win_height)

        cube2 = Cube([
            Vector3(0.5, 0.5, -0.5),
            Vector3(1, 0.5, -0.5),
            Vector3(1, 0, -0.5),
            Vector3(0.5, 0, -0.5),
            Vector3(0.5, 0.5, 0),
            Vector3(1, 0.5, 0),
            Vector3(1, 0, 0),
            Vector3(0.5, 0, 0)
        ], win_width, win_height)

        self._angle = 30

        self._cubes = [cube, cube2]

    def run(self):
        while True:
            for event in pygame.event.get():
                if event.type == pygame.QUIT:
                    pygame.quit()
                    sys.exit()

            self.clock.tick(50)
            self.screen.fill(Color.BLACK.value)

            for cube in self._cubes:
                transformed_vectors = cube.transform_vectors(self._angle)
                avg_z = cube.calculate_average_z(transformed_vectors)

                # Draw the faces using the Painter's algorithm:
                # Distant faces are drawn before the closer ones.
                for avg_z in sorted(avg_z, key=lambda x: x[1], reverse=True):
                    face_index = avg_z[0]
                    face = cube._faces[face_index]
                    pointlist = cube.create_polygon(face, transformed_vectors)

                    pygame.draw.polygon(self.screen, Color.SILVER.value,pointlist)
                    pygame.draw.polygon(self.screen, Color.BLACK.value, pointlist, 3)
                    # break 

            self._angle += 1

            pygame.display.flip()

if __name__ == "__main__":
    Simulation().run()

Both cubes should rotate around the Y-axis in this example. For the future I'd like to have a solution so they can rotate around any axis.

It is not sufficient to sort the faces of each cube separately by its depth. You've to sort the faces of all objects of the entire scene by its depth.

Create a list of tuples, which consists of the projected (transformed) points ofa face and the average depth (z value):

polygons = []
for cube in self._cubes:
    transformed_vectors = cube.transform_vectors(self._angle)
    avg_z = cube.calculate_average_z(transformed_vectors)
    for z in avg_z:
        face_index = z[0]
        face = cube._faces[face_index]
        pointlist = cube.create_polygon(face, transformed_vectors)
        polygons.append((pointlist, z[1]))

Draw the faces of all objects in (reverse) sorted order:

for poly in sorted(polygons, key=lambda x: x[1], reverse=True):
    pygame.draw.polygon(self.screen, Color.SILVER.value,poly[0])
    pygame.draw.polygon(self.screen, Color.BLACK.value, poly[0], 3)

Minimal example:

import math
import pygame

def project(vector, w, h, fov, distance):
    factor = math.atan(fov / 2 * math.pi / 180) / (distance + vector.z)
    x = vector.x * factor * w + w / 2
    y = -vector.y * factor * w + h / 2
    return pygame.math.Vector3(x, y, vector.z)

def rotate_vertices(vertices, angle, axis):
    return [v.rotate(angle, axis) for v in vertices]
def scale_vertices(vertices, s):
    return [pygame.math.Vector3(v[0]*s[0], v[1]*s[1], v[2]*s[2]) for v in vertices]
def translate_vertices(vertices, t):
    return [v + pygame.math.Vector3(t) for v in vertices]
def project_vertices(vertices, w, h, fov, distance):
    return [project(v, w, h, fov, distance) for v in vertices]

class Mesh():

    def __init__(self, vertices, faces):
        self.__vertices = [pygame.math.Vector3(v) for v in vertices]
        self.__faces = faces

    def rotate(self, angle, axis):
        self.__vertices = rotate_vertices(self.__vertices, angle, axis)
    def scale(self, s):
        self.__vertices = scale_vertices(self.__vertices, s)
    def translate(self, t):
        self.__vertices = translate_vertices(self.__vertices, t)

    def calculate_average_z(self, vertices):
        return [(i, sum([vertices[j].z for j in f]) / len(f)) for i, f in enumerate(self.__faces)]

    def get_face(self, index):
        return self.__faces[index]
    def get_vertices(self):
        return self.__vertices

    def create_polygon(self, face, vertices):
        return [(vertices[i].x, vertices[i].y) for i in [*face, face[0]]]
       
class Scene:
    def __init__(self, mehses, fov, distance):
        self.meshes = mehses
        self.fov = fov
        self.distance = distance 
        self.euler_angles = [0, 0, 0]

    def transform_vertices(self, vertices, width, height):
        transformed_vertices = vertices
        axis_list = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
        for angle, axis in reversed(list(zip(list(self.euler_angles), axis_list))):
            transformed_vertices = rotate_vertices(transformed_vertices, angle, axis)
        transformed_vertices = project_vertices(transformed_vertices, width, height, self.fov, self.distance)
        return transformed_vertices

    def draw(self, surface):
        
        polygons = []
        for mesh in self.meshes:
            transformed_vertices = self.transform_vertices(mesh.get_vertices(), *surface.get_size())
            avg_z = mesh.calculate_average_z(transformed_vertices)
            for z in avg_z:
            #for z in sorted(avg_z, key=lambda x: x[1], reverse=True):
                pointlist = mesh.create_polygon(mesh.get_face(z[0]), transformed_vertices)
                polygons.append((pointlist, z[1]))
                #pygame.draw.polygon(surface, (128, 128, 192), pointlist)
                #pygame.draw.polygon(surface, (0, 0, 0), pointlist, 3)

        for poly in sorted(polygons, key=lambda x: x[1], reverse=True):
            pygame.draw.polygon(surface, (128, 128, 192), poly[0])
            pygame.draw.polygon(surface, (0, 0, 0), poly[0], 3)
        

vertices = [(-1,-1,1), (1,-1,1), (1,1,1), (-1,1,1), (-1,-1,-1), (1,-1,-1), (1,1,-1), (-1,1,-1)]
faces = [(0,1,2,3), (1,5,6,2), (5,4,7,6), (4,0,3,7), (3,2,6,7), (1,0,4,5)]

cube_origins = [(-1, -1, 0), (0, -1, 0), (1, -1, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (-1, 1, 0), (-1, 0, 0)]
meshes = []
for origin in cube_origins:
    cube = Mesh(vertices, faces)
    cube.scale((0.5, 0.5, 0.5))
    cube.translate(origin)
    meshes.append(cube)

scene = Scene(meshes, 90, 5)

pygame.init()
window = pygame.display.set_mode((400, 300))
clock = pygame.time.Clock()

run = True
while run:
    clock.tick(60)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

    window.fill((255, 255, 255))
    scene.draw(window)
    scene.euler_angles[1] += 1
    pygame.display.flip()

pygame.quit()

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