修改一个公式从围绕一个圆周计算到一个椭圆？ [英] Modify a formula from calculating around a circle to around an oval?

问题描述

我在下面的函数中有这个公式。这是一个相当简单的概念，但这个公式让我差不多2个星期才能完美。它的作用是计算出一个物体在一定程度上和距离中心点的距离。手动绘制圆圈很有用，我也主要用于我的针距组件。它计算在哪里绘制针。

现在我试图找出如何修改这个公式来考虑椭圆或椭圆。我确实想到首先将组件绘制成圆形，然后在所有绘制后拉伸，但这不是一个干净的解决方案，因为我正在做的绘图已经是椭圆形的。 / p>

我需要为这个函数添加一个参数来告诉它的宽度/高度之间的比例，所以它知道如何偏离这一点。默认情况下，此参数应为1，表示Width = Height，表示无椭圆形图形或偏移量。但是假设我放2，这意味着宽度是高度的两倍，或1.5表示宽度是高度的1.5倍。

这是原来的功能： / p>

  function NewPosition（Center：TPoint; Distance：Integer; Degrees：Single）：TPoint; 
 var 
 Radians：Real; 
 begin 
 //将角度从度转换为弧度;减去135以使位置为0度
 Radians：=（度数 -  135）* Pi / 180; 
 Result.X：= Trunc（Distance * Cos（Radians）-Distance * Sin（Radians））+ Center.X; 
 Result.Y：= Trunc（Distance * Sin（Radians）+ Distance * Cos（Radians））+ Center.Y; 
结束
  

这里是需要添加的参数：

$ b $函数NewPosition（Center：TPoint; Distance：Integer; Degrees：Single;
OvalOffset：Single = 1）：TPoint;
var
Radians：Real;
begin
//将角度从度转换为弧度;减去135以使位置为0度
Radians：=（度数 - 135）* Pi / 180;
Result.X：= Trunc（Distance * Cos（Radians）-Distance * Sin（Radians））+ Center.X;
Result.Y：= Trunc（Distance * Sin（Radians）+ Distance * Cos（Radians））+ Center.Y;
结束

定义：

• 中心=从（椭圆中心）计算的中心点


• 距离=距离中心距离任何方向有多远， li>
  
• 学位=从右上角开始的中心点多少度


• OvalOffset =宽度和高度之间的差异比率

解决方案

将 OvalOffset 添加到结果中。 Y 公式...

  Result.Y：= Trunc（（Distance * Sin（Radians） +距离* Cos（Radians））/ OvalOffset）
 + Center.Y; 
  

I have this formula in a function below. It's a fairly simple concept, yet this formula took me almost 2 weeks to get perfect. What it does is calculates what point to place an object at a given degree around and distance from a central point. It's useful for manually drawing circles, and also I primarily use it for a needle gauge component of mine. It calculates where to draw the needle.

Now I'm trying to figure out how to modify this formula to take ovals or ellipses into account. I did think of the idea of drawing a component a round shape first, and then stretching it after everything's drawn, but this is not a clean solution, as the drawing which I'm doing will already be in the shape of an oval.

I need to add just one parameter to this function to tell it the ratio between the width/height so it knows how to off-set this point. By default, this parameter should be 1, meaning Width=Height, meaning no ovalish drawing or offset. But suppose I put 2, which means width is twice the size of the height, or 1.5 would mean the width is 1.5 times the height.

Here's the original function:

function NewPosition(Center: TPoint; Distance: Integer; Degrees: Single): TPoint;
var
  Radians: Real;
begin
  //Convert angle from degrees to radians; Subtract 135 to bring position to 0 Degrees
  Radians:= (Degrees - 135) * Pi / 180;
  Result.X:= Trunc(Distance*Cos(Radians)-Distance*Sin(Radians))+Center.X;
  Result.Y:= Trunc(Distance*Sin(Radians)+Distance*Cos(Radians))+Center.Y;
end;

Here it is with the added parameter I need:

function NewPosition(Center: TPoint; Distance: Integer; Degrees: Single;
  OvalOffset: Single = 1): TPoint;
var
  Radians: Real;
begin
  //Convert angle from degrees to radians; Subtract 135 to bring position to 0 Degrees
  Radians:= (Degrees - 135) * Pi / 180;
  Result.X:= Trunc(Distance*Cos(Radians)-Distance*Sin(Radians))+Center.X;
  Result.Y:= Trunc(Distance*Sin(Radians)+Distance*Cos(Radians))+Center.Y;
end;

DEFINITIONS:

• Center = Central point where to base calculations from (center of ellipse)
• Distance = How far from Center in any direction, regardless of Degrees
• Degrees = How many degrees around central point, starting from up-right
• OvalOffset = Ratio of difference between Width and Height

解决方案

Add a division by OvalOffset to just the Result.Y formula...

Result.Y:= Trunc((Distance*Sin(Radians)+Distance*Cos(Radians))/OvalOffset)
           +Center.Y;

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