无法从线性函数中获得正确的坐标

问题描述

我现在正在做的是将贝塞尔曲线和线的 100 个坐标点重新组合成一条折线，为此，我试图使用数学来生成放置在 1 个起点和起点之间的线上的点的坐标1 个终点。

问题是我得到了正确的 y 值、高于预期的 y 值和低于预期的 y 值，具体取决于直线上的情况（贝塞尔曲线工作正常），这是我现在的代码：

import pygame
from pygame import gfxdraw
from random import randint
from win32api import GetSystemMetrics
from time import time
import math
import numpy as np

width = GetSystemMetrics(0)
height = GetSystemMetrics(1)

def generate_original_points_coordinates(circle_size_px):
    generating = True
    while generating:
        x = randint(0,width)
        y = randint(0,height)
        if y < height-circle_size_px and y > circle_size_px and x < width-circle_size_px and x > circle_size_px:
            points.append([x,y])
            generating = False

def generate_points_coordinates(count,spacing,circle_size_px):
    for i in range(0,count-1):
        generating = True
        while generating:
            x = points[-1][0]+randint(-spacing,spacing)
            y = points[-1][1]+randint(-spacing,spacing)
            if y < height-circle_size_px and y > circle_size_px and x < width-circle_size_px and x > circle_size_px: 
                generating = False
                points.append([x,y])
        
def generate_original_and_p(count,circle_size_px):
    generate_original_points_coordinates(circle_size_px)
    generate_points_coordinates(count,circle_size_px)
    return points

running = True
while running:
    pygame.font.init()
    font = pygame.font.SysFont('freesansbold.ttf',32)
    text = font.render('NotBezier',True,(0,255))
    points = []
    gen_points = generate_original_and_p(9,800,234)
    size = [width,height]
    screen = pygame.display.set_mode(size,32)
    screen.fill((33,33,33))
    curve = []
    # Draw bezier curves from points in a list
    for i in range(0,len(gen_points)-2):
        dist_s = math.sqrt(math.pow(gen_points[i+2][0]-gen_points[i][0],2)+math.pow(gen_points[i+2][1]-gen_points[i][1],2))
        dist_x = gen_points[i+2][0] - gen_points[i][0]
        dist_y = gen_points[i+2][1] - gen_points[i][1]
        if dist_s < 234/2:
            line = []
            print(dist_s)
            gfxdraw.line(screen,gen_points[i][0],gen_points[i][1],gen_points[i+2][0],gen_points[i+2][1],255))
            m = (gen_points[i][1] - gen_points[i+2][1]) / (gen_points[i][0] - gen_points[i+2][0])
            b = np.linalg.norm(np.diff([gen_points[i],gen_points[i+2]],axis=0),axis=1).tolist()[0]
            for ratio in np.linspace(0,1,10):
                print("ratio = "+str(ratio)+",m = "+str(m)+",b = "+str(b)+",dist_x = "+str(dist_x)+",dist_y = "+str(dist_y))
                line.append([gen_points[i][0]+(ratio * dist_x),gen_points[i][1] + (m * (ratio * dist_y) + b)])
            curve.append(line)
        if i+2 == len(gen_points)-1:
            gfxdraw.filled_circle(screen,5,255,0))
            screen.blit(font.render(str(i+2),0)),(gen_points[i+2][0],gen_points[i+2][1]+10))
        gfxdraw.filled_circle(screen,0))
        screen.blit(font.render(str(i),(gen_points[i][0],gen_points[i][1]+10))

    pygame.display.flip()

    # Place points on such curves and lines

    print(gen_points)
    print(curve)
    print(len(curve))
    i = input("quit?: ")
    pygame.display.quit()
    if i == "quit":
        running = False

这是点 [[1059,559],[1472,684],[1090,509]] 的示例列表

这是创建行时的示例输出：

ratio = 0.0,m = -1.6129032258064515,b = 58.83026432033091,dist_x = 31,dist_y = -50
ratio = 0.1111111111111111,dist_y = -50
ratio = 0.2222222222222222,dist_y = -50
ratio = 0.3333333333333333,dist_y = -50
ratio = 0.4444444444444444,dist_y = -50
ratio = 0.5555555555555556,dist_y = -50
ratio = 0.6666666666666666,dist_y = -50
ratio = 0.7777777777777777,dist_y = -50
ratio = 0.8888888888888888,dist_y = -50
ratio = 1.0,dist_y = -50

# Points on screen

[
    [807,333],[1205,526],[1257,373],[1039,507],[724,834],[626,765],[1059,509]
]

# Coordinate of the 10 points located on that line and spaced by 10%

[
    [
         [1059.0,617.8302643203309],[1062.4444444444443,626.7908377970334],[1065.888888888889,635.7514112737359],[1069.3333333333333,644.7119847504384],[1072.7777777777778,653.6725582271409],[1076.2222222222222,662.6331317038434],[1079.6666666666667,671.593705180546],[1083.111111111111,680.5542786572485],[1086.5555555555557,689.514852133951],[1090.0,698.4754256106535]
     ]
]

如您所见，使用此函数的 y 横坐标高于预期，这只是许多情况中的一个案例。

是否知道导致此问题的原因以及如何解决？

TL:DR -> 使用 thisis 函数 https://pastebin.com/xgNLQiVt 在某些情况下获得不正确的 y 值

解决方法

猜猜 50K+ 提供某个函数的用法很复杂，因为我知道我也在我的代码中使用了 numpy，我找到了另一种方法来获得我想要的东西：

#  Generate 1000 x coordinates / Generate 1000 y coordinates

list_x,list_y = np.linspace(Points[i][0],Points[i+2][0],1000),np.linspace(Points[i][1],Points[i+2][1],1000)

#  Generate a list of coordinates out of list_x and list_y

line = [[list_x[i],list_y[i]] for i in range(1000)]

而且可能有一种更简单、更短的方法，我不知道获得相同的东西