取得svg/xaml arc的分数 [英] Get points of svg/xaml arc

问题描述

svg arc的格式(xaml中的弧具有相同的args):

Format of svg arc (arc in xaml have same args):

(rx ry x-axis-rotation large-arc-flag sweep-flag x y)

说明:

从当前点到(x，y)绘制一个椭圆弧.椭圆的大小和方向由两个半径(rx，ry)和x轴旋转定义，x轴旋转指示椭圆整体如何相对于当前坐标系旋转.椭圆的中心(cx，cy)是自动计算的，以满足其他参数施加的约束.大弧标记和扫掠标记有助于自动计算，并有助于确定圆弧的绘制方式.

Draws an elliptical arc from the current point to (x, y). The size and orientation of the ellipse are defined by two radii (rx, ry) and an x-axis-rotation, which indicates how the ellipse as a whole is rotated relative to the current coordinate system. The center (cx, cy) of the ellipse is calculated automatically to satisfy the constraints imposed by the other parameters. large-arc-flag and sweep-flag contribute to the automatic calculations and help determine how the arc is drawn.

我需要计算它的所有圆弧(当然，需要一些步骤).我该怎么办?我想用C#或Java进行编码.

I need to calc all point of it arc (with some step, of course). How I can do it? I would like to code on C# or on Java.

推荐答案

Bresenham算法是为逐点绘制而发明的.

Bresenham algorithm is invented for point-by-point drawing.

找到了一些用于旋转椭圆的代码(

Some code found for rotated ellipse (wayback machine)

已添加: 如何将以零为中心的椭圆转换为所需的隐式形式(A，B，C，D，E，F)

Added: How to transform zero-centered ellipse to needed implicit form (A,B,C,D,E,F)

A := (Cos(fi)/rx)^2 + (Sin(fi)/ry)^2;

C := (Sin(fi)/rx)^2 + (Cos(fi)/ry)^2;

B := Sin(2*fi)*(1/(ry*ry) - 1/(rx*rx));

D=E=0;

F:=-1

已检查rx = 100，ry = 60，fi = Pi/6:

Checked for rx=100, ry=60, fi=Pi/6:

另一步骤:Delphi函数获取任意椭圆的隐式形式. 我希望代码是可以理解的(Sqr(x)= x * x)

One more step: Delphi function to obtain implicit form for an arbitrary ellipse. I hope that code is understandable (Sqr(x) = x*x)

//calc implicit ellipse equation
//semiaxes rx, ry; rotated at fi radians; centered at (cx,cy)
//x = rx * Cos(t) * Cos(fi) - ry * Sin(t) * Sin(fi) + cx
//y = rx * Cos(t) * Sin(fi) + ry * Sin(t) * Cos(fi) + cy
//To obtain implicit equation, exclude t
//note: implicit form Ax^2+Bxy+Cy^2+Dx+Ey+F=0 (not 2B,2D,2E)

procedure CalcImplicitEllipseEquation(rx, ry, fi, cx, cy: Double;
                                      var A, B, C, D, E, F:  Double);
begin
  B := Sin(2 * Fi) * (ry * ry - rx * rx);
  A := Sqr(ry * Cos(fi)) + Sqr(rx * Sin(fi));
  C := Sqr(rx * Cos(fi)) + Sqr(ry * Sin(fi));
  D := -B * cy - 2 * A * cx;
  E := -2 * C * cy - B * cx;
  F := C * cy * cy + A * cx * cx + B * cx * cy - rx * rx * ry * ry;
end;

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