draw2d中的数学公式

图形就必然会存在几何的数学问题：点的旋转，求交点。

 

1、求点A(a,b)旋转β弧度后B的坐标:

	/**
	 * Returns a new transformed Point of the input Point based on the
	 * transformation values set.
	 */
	public Point getTransformed(Point p) {
		double x = p.x;
		double y = p.y;
		double temp;
		x *= scaleX;
		y *= scaleY;

		temp = x * cos - y * sin;
		y = x * sin + y * cos;
		x = temp;
		return new Point(Math.round(x + dx), Math.round(y + dy));
	}

 

 

a = cosα

b = sinα

x = cos(α + β) = cosα*cosβ - sinα*sinβ

y = sin(α + β) = sinα*cosβ + cosα*sinβ

=>

x = acosβ - bsinβ

y = bcosβ + asinβ

 

2、计算交点

（1）长方形外一点P以及长方形中心O，求PO的连线与长方形的交点：

	/**
	 * Gets a Rectangle from {@link #getBox()} and returns the Point where a
	 * line from the center of the Rectangle to the Point <i>reference</i>
	 * intersects the Rectangle.
	 */
	public Point getLocation(Point reference) {
		Rectangle r = Rectangle.SINGLETON;
		r.setBounds(getBox());
		r.translate(-1, -1);
		r.resize(1, 1);

		getOwner().translateToAbsolute(r);
		float centerX = r.x + 0.5f * r.width;
		float centerY = r.y + 0.5f * r.height;

		if (r.isEmpty() || (reference.x == (int) centerX && reference.y == (int) centerY))
			return new Point((int) centerX, (int) centerY); // This avoids divide-by-zero

		float dx = reference.x - centerX;
		float dy = reference.y - centerY;

		// r.width, r.height, dx, and dy are guaranteed to be non-zero.
		float scale = 0.5f / Math.max(Math.abs(dx) / r.width, Math.abs(dy) / r.height);

		dx *= scale;
		dy *= scale;
		centerX += dx;
		centerY += dy;

		return new Point(Math.round(centerX), Math.round(centerY));
	}

 

1> 判断象限（dx,dy的符号可以确定）

2> 与那条边相交:

float scale = 0.5f / Math.max(Math.abs(dx) / r.width, Math.abs(dy) / r.height);

根据比例算出大边！然后通过相似三角形进行计算。

 

(2) 椭圆外一点P以及椭圆中心O，求PO的连线与椭圆的交点：

	/**
	 * Returns a point on the ellipse (defined by the owner's bounding box)
	 * where the connection should be anchored.
	 */
	public Point getLocation(Point reference) {
		Rectangle r = Rectangle.SINGLETON;
		r.setBounds(getOwner().getBounds());
		r.translate(-1, -1);
		r.resize(1, 1);
		getOwner().translateToAbsolute(r);

                // 相当于 
                // ref.x = reference.x - r.getCenter().x; 
                // ref.y = reference.y - r.getCenter().y;
		Point ref = r.getCenter().negate().translate(reference);

		if (ref.x == 0)
			return new Point(reference.x, (ref.y > 0) ? r.bottom() : r.y);
		if (ref.y == 0)
			return new Point((ref.x > 0) ? r.right() : r.x, reference.y);

		float dx = (ref.x > 0) ? 0.5f : -0.5f;
		float dy = (ref.y > 0) ? 0.5f : -0.5f;

		// ref.x, ref.y, r.width, r.height != 0 => safe to proceed

		float k = (float) (ref.y * r.width) / (ref.x * r.height);
		k = k * k;

		return r.getCenter().translate((int) (r.width * dx / Math.sqrt(1 + k)),
				(int) (r.height * dy / Math.sqrt(1 + 1 / k)));
	}

 

1>计算角度θ；

2>通过椭圆的三角坐标代换算出坐标值。