Python中的2D矢量投影

Question

下面的代码将蓝色矢量AC投影到红色矢量AB上,得到的投影矢量AD被绘制为紫色.这是我自己实现的Wolfram演示.

然而有些事情是错的,我可以真正弄清楚是什么.应该是投影公式本身是错误的,或者我错误地将一些局部坐标与世界坐标错误.任何帮助表示赞赏.

假设你有pygame,这个代码被修剪但仍然可以没有问题地执行:

import pygame
from pygame.locals import *

def vadd(a,b):
    return (a[0]+b[0],a[1]+b[1])

def vsub(a,b):
    return (a[0]-b[0],a[1]-b[1])

def project(a, b):
    """ project a onto b
        formula: b(dot(a,b)/(|b|^2))
    """
    abdot = (a[0]*b[0])+(a[1]*b[1])
    blensq = (b[0]*b[0])+(b[1]*b[1])

    temp = float(abdot)/float(blensq)
    c = (b[0]*temp,b[1]*temp)

    print a,b,abdot,blensq,temp,c
    return c

pygame.init()
screen = pygame.display.set_mode((150, 150))
running = True

A = (75.0,75.0)
B = (100.0,50.0)
C = (90,70)

AB = vsub(B,A)
AC = vsub(C,A)

D = project(AC,AB)
AD = vsub(D,A)

while running:
    for event in pygame.event.get():
        if event.type == QUIT or (event.type == KEYDOWN and event.key == K_ESCAPE):
            running = False

    pygame.draw.line(screen, (255,0,0), A, B)
    pygame.draw.line(screen, (0,0,255), A, C)
    pygame.draw.line(screen, (255,0,255), A, D)
    pygame.display.flip()

Answer 1

不应该这样

D = project(AC,AB)
AD = vsub(D,A)

是

AD = project(AC,AB)
D = vadd(A,AD)

不幸的是,我无法测试它,但这是我唯一看错了.