如何在3D空间中围绕X轴旋转正方形

问题描述

所以我一直在尝试学习3D渲染的工作原理。我尝试编写一个脚本，目标是在3D空间中旋转平面（2D）正方形。我首先在标准化空间（-1，1）中定义一个正方形。请注意，只有x和y被归一化。

class Vec3:
    #  3D VECTOR
    def __init__(self,x,y,z):
        self.x = x
        self.y = y
        self.z = z

s = 1
p1 = Vec3(-s,-s,-s) 
p2 = Vec3(s,-s)
p3 = Vec3(s,s,-s)
p4 = Vec3(-s,-s)

然后将这些点翻译到屏幕中

p1.z += 6
p2.z += 6
p3.z += 6
p4.z += 6

此后的所有操作都在应用程序循环内完成。我使用以下功能应用投影来将点缩放到屏幕上：

class Transform:
    # IT TRANSFORMS THE X AND Y FROM NORMALISED SPACE TO SCREEN SPACE WITH PROJECTION APPLIED 
    def worldSpaceTransform(self,vec3,w,h):
        if vec3.z == 0:
            vec3.z = 0.001
        zInverse = 1/ vec3.z
        xTransformed = ((vec3.x * zInverse) + 1) * (w/2)
        yTransformed = ((-vec3.y * zInverse) + 1) * (h/2)
        xTransformed = str(xTransformed)[:6]
        yTransformed = str(yTransformed)[:6]
        return Vec2(float(xTransformed),float(yTransformed))

像这样：

# TRANSLATING THE SQUARE SHEET INTO THE SCREEN SPACE
    point1 = transform.worldSpaceTransform(p1,SCREENWIDTH,SCREENHEIGHT)
    point2 = transform.worldSpaceTransform(p2,SCREENHEIGHT)
    point3 = transform.worldSpaceTransform(p3,SCREENHEIGHT)
    point4 = transform.worldSpaceTransform(p4,SCREENHEIGHT)

并指出要点：

# STORING THE POINTS TO A TUPLE SO IT CAN BE DRAWN USING pygame.draw.lines
    points = ((point1.x,point1.y),(point2.x,point2.y),(point3.x,point3.y),(point4.x,point4.y),(point1.x,point1.y))
    pygame.draw.lines(D,(0,0),False,points)

（我认为）到目前为止，所有方法都可以正常工作，因为它按照预期的方式绘制了一个正方形。

现在旋转。我尝试了所有轴的旋转，但没有一个起作用，但是为了具体起见，我将讨论x轴。以下是旋转类。我从维基百科复制了旋转矩阵。我不确定它们如何工作，因此我也不知道它是否与我上面描述的系统兼容。

def multVecMatrix(vec3,mat3):
    # MULTIPLIES A Vec3 OBJECT WITH Mat3 OBJECT AND RETURNS A NEW Vec3  ? 
    x = vec3.x * mat3.matrix[0][0] + vec3.y * mat3.matrix[0][1] + vec3.z * mat3.matrix[0][2]
    y = vec3.x * mat3.matrix[1][0] + vec3.y * mat3.matrix[1][1] + vec3.z * mat3.matrix[1][2]
    z = vec3.x * mat3.matrix[2][0] + vec3.y * mat3.matrix[2][1] + vec3.z * mat3.matrix[2][2]
    return Vec3(x,z)

class Rotation:
    def rotateX(self,theta):
        # ROTATION MATRIX IN X AXIS ??
        sinTheta = sin(theta)
        cosTheta = cos(theta)
        m = Mat3()
        m.matrix = [[1,0],[0,cosTheta,sinTheta],-sinTheta,cosTheta]]
        return m

    def rotate(self,theta,axis=None):
        # ROTATES A Vec3 BY GIVEN THETA AND AXIS ??
        if axis == "x":
            return multVecMatrix(vec3,self.rotateX(theta))
        if axis == "y":
            return multVecMatrix(vec3,self.rotateY(theta))
        if axis == "z":
            return multVecMatrix(vec3,self.rotateZ(theta)) 

在将屏幕填满白色之后，再将点从标准化空间缩放到屏幕空间之前，这样称呼它。

    # screen is filled with white color
    # ROTATING THE POINTS AROUND X AXIS ?????

    p1.x = rotation.rotate(p1,thetax,axis='x').x
    p1.y = rotation.rotate(p1,thetay,axis='x').y
    p1.z = rotation.rotate(p1,axis='x').z

    p2.x = rotation.rotate(p2,axis='x').x
    p2.y = rotation.rotate(p2,axis='x').y
    p2.z = rotation.rotate(p2,axis='x').z

    p3.x = rotation.rotate(p3,axis='x').x
    p3.y = rotation.rotate(p3,axis='x').y
    p3.z = rotation.rotate(p3,axis='x').z

    p4.x = rotation.rotate(p4,axis='x').x
    p4.y = rotation.rotate(p4,axis='x').y
    p4.z = rotation.rotate(p4,axis='x').z
    
    # then the points are translated into world space

应用旋转后，看起来它正在移动并绕着x轴旋转，但没有旋转。我希望它旋转并保持原样。我在做什么错了？

完整的复制粘贴代码以供参考：

import pygame
from math import sin,cos,radians
pygame.init()

### PYGAME STUFF ######################################

SCREENWIDTH = 600
SCREENHEIGHT = 600
D = pygame.display.set_mode((SCREENWIDTH,SCREENHEIGHT))
pygame.display.set_caption("PRESS SPACE TO ROTATE AROUND X")

######### MATH FUNCTIONS AND CLASSES ####################

class Mat3:
    # 3X3 MATRIX INITIALIZED WITH ALL 0's
    def __init__(self):
        self.matrix = [[0 for i in range(3)],[0 for i in range(3)],[0 for i in range(3)]]

class Vec2:
    # 2D VECTOR
    def __init__(self,y):
        self.x = x
        self.y = y

class Vec3:
    #  3D VECTOR
    def __init__(self,z):
        self.x = x
        self.y = y
        self.z = z

def multVecMatrix(vec3,mat3):
    # MULTIPLIES A Vec3 OBJECT WITH Mat3 OBJECT AND RETURNS A NEW Vec3 
    x = vec3.x * mat3.matrix[0][0] + vec3.y * mat3.matrix[0][1] + vec3.z * mat3.matrix[0][2]
    y = vec3.x * mat3.matrix[1][0] + vec3.y * mat3.matrix[1][1] + vec3.z * mat3.matrix[1][2]
    z = vec3.x * mat3.matrix[2][0] + vec3.y * mat3.matrix[2][1] + vec3.z * mat3.matrix[1][2]
    return Vec3(x,z)

class Transform:
    # IT TRANSFORMS THE X AND Y FROM NORMALIZED SPACE TO SCREEN SPACE WITH PROJECTION APPLIED
    def worldSpaceTransform(self,float(yTransformed))

class Rotation:
    def rotateX(self,theta):
        # ROTATION MATRIX IN X AXIS
        sinTheta = sin(theta)
        cosTheta = cos(theta)
        m = Mat3()
        m.matrix = [[1,axis=None):
        # ROTATES A Vec3 BY GIVEN THETA AND AXIS
        if axis == "x":
            return multVecMatrix(vec3,self.rotateZ(theta))

transform = Transform()
rotation = Rotation()


# ASSIGNING 4 Vec3's FOR 4 SIDES OF SQUARE IN NORMALIZED SPACE
s = 1
p1 = Vec3(-s,-s)

# TRANSLATING THE POINTS OF THE CUBE A LITTLE BIT INTO THE SCREEN
p1.z += 6
p2.z += 6
p3.z += 6
p4.z += 6

# ASSIGNING THE ROTATION ANGLES
thetax = 0

# APPLICATION LOOP
while True:
    pygame.event.get()
    D.fill((255,255,255))


    # ROTATING THE POINTS AROUND X AXIS

    p1.x = rotation.rotate(p1,axis='x').z
    

    # TRANSLATING THE SQUARE SHEET INTO THE SCREEN SPACE
    point1 = transform.worldSpaceTransform(p1,SCREENHEIGHT)

    # STORING THE POINTS TO A TUPLE SO IT CAN BE DRAWN USING pygame.draw.lines
    points = ((point1.x,point1.y))

    
    keys = pygame.key.get_pressed()
    # ROTATE X ?
    if keys[pygame.K_SPACE]:
        thetax -= 0.005

    pygame.draw.lines(D,points)
    
    pygame.display.flip()

解决方法

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