结果

总结

网上都很容易找到一点、两点透视投影的变换矩阵，唯独三点透视矩阵不好找，偏偏发现一个却是和两点的矩阵一样，阿巴阿巴。。。。也没有办法给人家留言说你贴错图了emmmm，最后只好通读几个PPT总结了一下三点透视变换的矩阵，就是下面几个矩阵的乘积

# 平移到LMN
mtranslation = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [L, M, N, 1]], dtype='float32')
# 沿y轴旋转
mrotatey = np.array([[math.cos(xita), 0, -math.sin(xita), 0], [0, 1, 0, 0],[math.sin(xita), 0, math.cos(xita), 0], [0, 0, 0, 1]],dtype='float32')
# 沿x轴旋转
mrotatex = np.array([[1, 0, 0, 0], [0, math.cos(five), math.sin(five), 0],[0, -math.sin(five), math.cos(five), 0], [0, 0, 0, 1]],dtype='float32')
# 透视
mperspective = np.array([[1, 0, 0, P], [0, 1, 0, Q], [0, 0, 1, R], [0, 0, 0, 1]], dtype='float32')
# 向xoy平面做正投影
mprojectionxy = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]], dtype='float32')

然后numpy的矩阵相乘是np.matmul，元素相乘是np.multiply或者*，第一天用后者算出来的结果整得我人傻了
角度表示是先将派分割成180再乘，比如30度是这样表示的degree = math.pi / 180 * 30，而不是degree = 30

源代码

后续如果有更新，最新代码都在我的Github仓库

#!/usr/bin/env python3
# -*- encoding: utf-8 -*-
'''
@File    :  perspectiveone.py
@Time    :  2020/12/11 21:45:11
@Author  :  Kearney
@Version :  0.0.0
@Contact :  191615342@qq.com
@License :  GPL 3.0
@Desc    :  一点透视、两点透视画布横轴x向右增大，纵轴y向下增大ref:    https://blog.csdn.net/mylovestart/article/details/8352105https://wenku.baidu.com/view/ce28831e0508763230121275.htmlhttps://www.cnblogs.com/Penglimei/p/9750390.html
'''
import pygame
import sys
import numpy as np
import math# 长方体的八个点(x, y ,z, 1)，其他点数的立体图形需要修改draw的参数
points = [[0, 0, 200, 1], [200, 0, 200, 1], [200, 0, 0, 1], [0, 0, 0, 1],[0, 200, 200, 1], [200, 200, 200, 1], [200, 200, 0, 1],[0, 200, 0, 1]]onepoint = []  # 一点透视后的二维坐标
twopoint = []  # 两点透视后的二维坐标
threepoint = []  # 三点透视后的二维坐标# 一点透视参数
L = 100  # 平移位置L, M, N
M = 100
N = 100
D = 300  # 视距
# 两点透视参数
P = 2
R = 3
xita = math.pi / 180 * 65  # 角度xita
Q = 1.5  # 三点透视参数
five = math.pi / 180 * 80  # 角度five，三点透视参数# 一点透视变换矩阵
transMatrix = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1 / D], [L, M, 0, 1 + (N / D)]],dtype='float32')# 一点透视：将三维坐标映射到二维
for e in range(0, len(points)):tmp = np.matmul(np.array(points[e], dtype='float32'), transMatrix)tmp = tmp / tmp[3]  # 齐次化onepoint.append(tmp.tolist()[:2])# 两点透视变换矩阵
twoMatrix = np.array([[math.cos(xita), 0, 0,(P * math.cos(xita) - R * math.sin(xita))], [0, 1, 0, 0],[math.sin(xita), 0, 0, (P * math.sin(xita) + R * math.cos(xita))],[(L * math.cos(xita) + N * math.sin(xita)), M, 0,(P * (L * math.cos(xita) + N * math.sin(xita))) +(R * (N * math.cos(xita) + L * math.sin(xita))) + 1]],dtype='float32')
# 两点透视降维变换
for e in range(0, len(points)):tmp = np.matmul(np.array(points[e], dtype='float32'), twoMatrix)tmp = tmp / tmp[3]  # 齐次化tmp = tmp * 500  # 非必须：放大，太小看不见tmp[0] += 200  # 非必须：整体向右平移，不然和一位透视挡在一起了twopoint.append(tmp.tolist()[:2])# 三点透视变换矩阵
# 平移到LMN
mtranslation = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [L, M, N, 1]], dtype='float32')
# 沿y轴旋转
mrotatey = np.array([[math.cos(xita), 0, -math.sin(xita), 0], [0, 1, 0, 0],[math.sin(xita), 0, math.cos(xita), 0], [0, 0, 0, 1]],dtype='float32')
# 沿x轴旋转
mrotatex = np.array([[1, 0, 0, 0], [0, math.cos(five), math.sin(five), 0],[0, -math.sin(five), math.cos(five), 0], [0, 0, 0, 1]],dtype='float32')
# 透视
mperspective = np.array([[1, 0, 0, P], [0, 1, 0, Q], [0, 0, 1, R], [0, 0, 0, 1]], dtype='float32')
# 向xoy平面做正投影
mprojectionxy = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]], dtype='float32')
threeMatrix = np.matmul(np.matmul(np.matmul(np.matmul(mtranslation, mrotatey), mrotatex),mperspective), mprojectionxy)# 三点透视降维变换
for e in range(0, len(points)):tmp = np.matmul(np.array(points[e], dtype='float32'), threeMatrix)tmp = tmp / tmp[3]  # 齐次化tmp = tmp * 800  # 非必须：放大，太小看不见tmp[0] += 600  # 非必须：整体向右平移，不然和一点透视挡在一起了tmp[1] += 100  # 非必须：整体向下平移，不然和一点透视挡在一起了threepoint.append(tmp.tolist()[:2])LINECOLOR = (29, 244, 255)  # 颜色设置
BACKYCOLOR = (255, 212, 238)
LINEWIDTH = 3  # 线宽
pygame.init()
screen = pygame.display.set_mode((920, 640))while True:screen.fill(BACKYCOLOR)# 一点透视的图pygame.draw.lines(screen, LINECOLOR, False, onepoint, LINEWIDTH)  # 懒人划线pygame.draw.line(screen, BACKYCOLOR, onepoint[3], onepoint[4],LINEWIDTH)  # 遮瑕# 补全剩下的线条pygame.draw.line(screen, LINECOLOR, onepoint[0], onepoint[3], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, onepoint[4], onepoint[7], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, onepoint[0], onepoint[1], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, onepoint[0], onepoint[1], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, onepoint[0], onepoint[4], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, onepoint[3], onepoint[7], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, onepoint[2], onepoint[6], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, onepoint[1], onepoint[5], LINEWIDTH)# 两点透视的图pygame.draw.lines(screen, LINECOLOR, False, twopoint, LINEWIDTH)pygame.draw.line(screen, BACKYCOLOR, twopoint[3], twopoint[4], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, twopoint[0], twopoint[3], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, twopoint[4], twopoint[7], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, twopoint[0], twopoint[1], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, twopoint[0], twopoint[1], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, twopoint[0], twopoint[4], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, twopoint[3], twopoint[7], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, twopoint[2], twopoint[6], LINEWIDTH)pygame.draw.line(screen, LINECOLOR, twopoint[1], twopoint[5], LINEWIDTH)pygame.draw.lines(screen, LINECOLOR, False, threepoint, LINEWIDTH)pygame.draw.line(screen, BACKYCOLOR, threepoint[3], threepoint[4],LINEWIDTH)pygame.draw.line(screen, LINECOLOR, threepoint[0], threepoint[3],LINEWIDTH)pygame.draw.line(screen, LINECOLOR, threepoint[4], threepoint[7],LINEWIDTH)pygame.draw.line(screen, LINECOLOR, threepoint[0], threepoint[1],LINEWIDTH)pygame.draw.line(screen, LINECOLOR, threepoint[0], threepoint[1],LINEWIDTH)pygame.draw.line(screen, LINECOLOR, threepoint[0], threepoint[4],LINEWIDTH)pygame.draw.line(screen, LINECOLOR, threepoint[3], threepoint[7],LINEWIDTH)pygame.draw.line(screen, LINECOLOR, threepoint[2], threepoint[6],LINEWIDTH)pygame.draw.line(screen, LINECOLOR, threepoint[1], threepoint[5],LINEWIDTH)for event in pygame.event.get():if event.type == pygame.QUIT:pygame.quit()sys.exit(0)pygame.display.update()

一点、两点、三点透视投影的python3实现-计算机图形学相关推荐

点积和叉积在计算机图形学的应用
点积和叉积在计算机图形学中,是最为基础且重要的概念,初学者弄清它的概念的应用,是很重要的.最后一节,是为了加强理解记录,如果不看也是可以的,大家选择观看,有兴趣可以去看原视频,结合我的笔记. 前置知识 ...
一点、两点、三点透视投影
在图形学的书上看到一点.两点.三点透视投影,有一些公式推理,但都是把模型放在某个特定地方推导投影矩阵,实践中我发现,用一般的透视投影,把相机放到特定地方,就可以实现一点.两点.三点透视投影.这样就不需 ...
计算机图形学基础之一点两点三点透视图
嘿嘿,如果你想应付一下这个计算机图形学的作业,那么这篇文章在合适不过了. 想看懂代码,那么只需要明白齐次坐标在各种变换下的变化即可. 对了,别忘记在java工程中补上一张"backgroun ...
计算机图形学学习笔记（八）：三维图形变换：三维几何变换，投影变换（平行/ 透视投影）
接上文计算机图形学学习笔记(七):二维图形变换:平移,比例,旋转,坐标变换等通过三维图形变换,可由简单图形得到复杂图形,三维图形变化则分为三维几何变换和投影变换. 6.1 三维图形几何变换三维 ...
计算机图形学-3D观察与图像渲染流水线-投影全解析
本文目标: 理清OpenGL在3D观察的整个流程. 清楚各个专业术语的含义. 对坐标系变换的数学有所掌握. 1 三维观察与观察流程 1.1 三维观察与照相观察的对比三维观察过程与使用照相机拍摄照片类 ...
计算机图形学三维投影程序,三维计算机图形学
<三维计算机图形学>是科学出版社出版.本书共分17章,内容包括IDE环境与编程基础.基本语法与数据类型.运算操作.流程控制.面向对象程序设计.用户界面编程.文件系统管理.图形图像多媒体编程 ...
【计算机图形学基础】投影矩阵
最近在重温计算机图形学的基础知识,期望能做到温故知新,加深对其的理解,以便能从容应对工作中各种情况. 小弟水平有限,若有不正确之处,欢迎大家批评指正. 相关文章链接: [计算机图形学基础]线性 ...
《每天一点学习笔记》-初学python3～3
<每天一点学习笔记>-初学python3 这几天乱遭事有点多,没来得及写,就不写第几天了,综合整理一下,简单记录这几天学的内容吧.简单来说我看了一些入门的基础知识,有的是视频,也有别人写的 ...
计算机图形学作业一：旋转与投影
计算机图形学作业一:旋转与投影文章目录计算机图形学作业一:旋转与投影 1.题目概述: 2.知识储备: 2.1 MVP变换 2.2罗德里格斯旋转公式 3.解答过程: 4.总结思考: 1.题目概述 ...

一点、两点、三点透视投影的python3实现-计算机图形学

结果

总结

源代码

一点、两点、三点透视投影的python3实现-计算机图形学相关推荐

最新文章

热门文章