计算将一个矩形的point1（x，y坐标）转换为不同矩形的Point1（x，y）的缩放因子 [英] Calculate scaling factor for converting point1( x,y coordinates) of one rectangle to Point1( x,y) of a different rectangle

问题描述

将一个矩形的x，y坐标缩放到其他矩形坐标的过程非常简单，如在此链接中更好地解释

http://www.icoachmath.com/math_dictionary/scale_factor.html

<如果我们有两个矩形，则有Maxwidth：2000和Maxheight：1000

，第二个矩形的大小MaxWidth：4000和MaxHeight = 2000

所以用于将rect1的坐标转换为rect2的缩放因子为

为rect2中的x：rect1中的x Rect1的Rect2 / MaxWidht）
在rect2中的y：（rect1中的y）*（Rect2的MaxHeight / Rect1的MaxHeight）

因此当一个矩形中心的

是原点（X，Y - 0,0）将位于中心，并且x和y也将为负值你从中心向左移动，然后x将是负的，在右边，它将是正的相同的Y，如果你向上，那么y将是积极的，但如果你去底部，那么Y将是负的，所以这个矩形的范围趋向to（
-MaxWidth to + MaxWidth，-MaxHeight to + MaxHeight）

现在我们有第二个矩形，其中心位于最左边， b $ b（最左边和最上-0.0），因为我们必须沿着x轴向右移动，沿着y轴向下移动，所以x和y总是为正值。

因此，如何计算将原点在矩形中心（MaxWidth / 2，MaxHeight / 2）的矩形的坐标转换为原点最左边和最顶点的矩形的比例因子位置

解决方案

让我们先来看一个矩形的坐标是两个对角线：
X0_Old，Y0_Old）和（X1_Old，Y1_Old）
，第二个 -
（X0_New，Y0_New） c $ c>

那么坐标转换将类似于

 每个点：$ b​​ $ b X_New = X0_New +（X_Old -X0_Old）* X_Coeff 
其中
 X_Coeff =（X1_New -X0_New）/（X1_Old -X0_Old）
  

（和Y坐标相同）

Process of scaling x,y coordinates of one rectangle to other rectangle coordinates is pretty simple as better explained at this link

http://www.icoachmath.com/math_dictionary/scale_factor.html

if we have two rectangle one is having Maxwidth: 2000 and Maxheight: 1000

and second rectangle of size MaxWidth : 4000 and MaxHeight = 2000

so scale factor for converting coordinate of rect1 to rect2 would be

for x in rect2 : (x in rect1) * (MaxWidth of Rect2/ MaxWidht of Rect1) for y in rect2 : (y in rect1) * (MaxHeight of Rect2/ MaxHeight of Rect1)

but what should be scale factor when

for one rectangle center is origin(X,Y - 0,0) would be at the center and there would be negative values for x and y as well if you go left from center then x would be in negative and in right side it would be positive same for Y, if you go up then y would be positive but if you go to bottom, thenY Would be negative, so extents of this rectangle tends to ( -MaxWidth to +MaxWidth, -MaxHeight to +MaxHeight)

Now we have second rectangle which is having center at most left and top most position (most left and top most-0,0) and as we have to travel in right direction along x axis and down along y axis, So there would be always positive values for x and y.

So, how to calculate scale factor for converting coordiantes of rectangle which has the origin at center of rectanlge(MaxWidth/2,MaxHeight/2) to the rectanlge which has origin at most left and top most position

解决方案

Let's first rectangle has coordinates of two (diagonal opposite) corners: (X0_Old, Y0_Old) and (X1_Old, Y1_Old) and the second one - (X0_New, Y0_New) and (X1_New, Y1_New)

then coordinate transformation will look like

for every point:
  X_New = X0_New + (X_Old - X0_Old) * X_Coeff
where 
  X_Coeff = (X1_New - X0_New) / (X1_Old - X0_Old)

(and tha same for Y-coordinates)

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