如何检查三个点是否形成一条直线? [英] How do I check to see if three points form a straight line?

问题描述

问题:创建具有六个输入的函数mylinecheck(a,b,c,d,e,f): a,b,c,d,e,f是实数，而a,c,e不相等.该函数必须检查三个点(a,b)，(c,d)和(e,f)是否都位于同一行上.如果是，则返回1.如果不是，则返回0.

Problem: Create the function mylinecheck(a,b,c,d,e,f) which takes six inputs: a,b,c,d,e,f which are real numbers, and a,c,e are not equal. The function must check if the three points (a,b), (c,d), and (e,f) all lie on the same line. If so, return a 1. If not, return a 0.

我想我想做的就是告诉MATLAB检查坐标(c,d)和(e,f)是否为(a,b)的倍数，如果不是，我将返回0.如果是，则将返回1.如果这是正确的思考过程，那么我不确定如何命令MATLAB这样做.任何建议将不胜感激.

I think what I want to do is tell MATLAB to check if coordinates (c,d) and (e,f) are multiples of (a,b), and then if not I will return a 0. If so, I will return a 1. If this is the right thought process, I'm not sure how to command MATLAB to do so. Any advice would be greatly appreciated.

推荐答案

(x1,y1)，(x2,y2)和(x3,y3)点在且仅当满足时位于同一行上

The points (x1,y1), (x2,y2), and (x3,y3) lie on the same line if and only if they satisfy

a x + b y + c = 0

用于a，b和c的固定值(我无法克服您的表示法；对混乱"表示抱歉)，其中a或b为非零.因此，当且仅当

for fixed values of a, b, and c (I cannot get over your notation; sorry for the "confusion"), where a or b are nonzero. Hence they lie on the same line if and only if

a x1 + b y1 + c = 0         [x1 y1 1][a]   [0]
a x2 + b y2 + c = 0   <=>   [x2 y2 1][b] = [0]
a x3 + b y3 + c = 0         [x3 y3 1][c]   [0],

即具有矩阵的齐次线性系统

that is, the homogeneous linear system with the matrix

    [x1 y1 1]
X = [x2 y2 1]
    [x3 y3 1]

具有非零解.仅当X为单数时，才有可能.通过消除X的最后一列，您可以发现X是单数的，当且仅当矩阵

has a nonzero solution. This is possible only if X is singular. By eliminating the last column of X you can find that X is singular if and only if the matrix

Y = [x2-x1 y2-y1]
    [x3-x1 y3-y1]

是单数.

要在Matlab中可靠地检查矩阵的奇异性，可以使用SVD或等效的函数rank.因此，您的功能可以按以下方式实现:

To reliably check for the singularity of a matrix in Matlab, you can use SVD or, equivalently, the function rank. Hence your function could be implemented as follows:

function [result] = mylinecheck(x1,y1,x2,y2,x3,y3)

result = rank([x2-x1, y2-y1; x3-x1, y3-y1]) < 2;

这篇关于如何检查三个点是否形成一条直线?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！