改变坐标系 [英] Changing co-ordinate system

问题描述

我需要从上面显示的XY坐标系统切换到使用System :: Drawing :: Drawing2D（即GDI +）的X'Y'坐标系统。这是我想到的：

I need to switch from the XY co-ordinate system shown above to the X'Y' co-ordinate system using System::Drawing::Drawing2D (i.e. GDI+). This is what I have in mind:

float rotation =                    // +90 below is because AB is the new vertical...
    Math::Atan2(pB.Y - pA.Y, pB.X - pA.X) * 180.0 / Math::PI + 90.0f;

Matrix m;
m.Translate(pA.X, pA.Y);
m.Rotate(rotation);
m.Invert();

array<PointF> points = gcnew array<PointF>{ pC };
m.TransformPoints(points);

有最小化舍入错误的方法吗？我可以避免 Atan2 （或其他反三角函数）调用吗？

Is there a way to do this while minimizing rounding errors? Can I avoid the Atan2 (or other inverse trigonometric function) call here?

推荐答案

我不熟悉gdi +，但原则上你可以做这个没有反向trig或操作符反转。 （我说操作符反转而不是矩阵反转，因为 Matrix 看起来不像是一个矩阵。）

I'm not familiar with gdi+, but in principle you can do this without inverse trig or operator inversion. (I say "operator inversion" instead of "matrix inversion" because this Matrix doesn't look like a matrix to me.)

首先，你应该能够通过改变你定义运算符的方式来避免矩阵求逆。这里有一个盲目的刺：

First, you should be able to avoid the matrix inversion by changing the way you define the operator. Here's a blind stab at it:

Matrix m;
m.Rotate(-rotation);
m.Translate(-pA.X, -pA.Y);

现在对于旋转本身，通常的方法是使用一个矩阵，

Now for the rotation itself, the usual way to do it is with a matrix that looks like this:

cos(theta)  -sin(theta)
sin(theta)   cos(theta)

您正在使用atan（y / x）计算theta。但是如果你想要的是罪和cos，你可以正规化x和y并直接使用它们：

and you're calculating theta using atan(y/x). But if what you want are the sin and cos, you can just normalize x and y and use them directly:

x  -y
y   x

不需要atan。 其实，根本没有trig！

这篇关于改变坐标系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！