如何计算 java.awt.geom.Area 的面积?

问题描述

我正在寻找一种方法来计算 java.awt.geom.Area 的任意实例的面积(以像素为单位).

I am looking for a way to calculate the area, in pixels, of an arbitrary instance of java.awt.geom.Area.

背景:我的应用程序中有可能重叠的 Shape.我想知道一个 Shape 与另一个重叠多少.Shape 可能会倾斜、旋转等.如果我有一个函数 area(Shape)(或 Area)，我可以使用两个 Shape 的交集如下:

The background: I have Shapes in my applications that may overlap. I want to know how much one Shape overlaps another. The Shapes may be skewed, rotated, etc. If I had a function area(Shape) (or Area), I could use the intersection of two Shapes like so:

double fractionObscured(Shape bottom, Shape top) {
    Area intersection = new Area(bottom);
    intersection.intersect(new Area(top));
    return area(intersection) / area(bottom);
}

推荐答案

一种方法是 fill() 每个都按比例缩放和 转换 Shape 使用合适的 AlphaComposite 和计算底层 中的重叠像素光栅.

One approach would be to fill() each scaled and transformed Shape with a different color using a suitable AlphaComposite and count the overlapping pixels in the underlying Raster.

附录1:使用这个计算器查看AlphaComposite.Xor表明任意两种不透明颜色的交集为零.

Addendum 1: Using this calculator to see the effect of AlphaComposite.Xor shows that the intersetion of any two opaque colors is zero.

附录2:计数像素可能存在性能问题；采样可能会有所帮助.如果每个 Shape 是相当凸的，可以从 intersect() 面积为 的面积之和Shapes' getBounds2D().例如，

Addendum 2: Counting pixels may have performance problems; sampling may help. If each Shape is reasonably convex, it may be possible to estimate the overlap from the ratio of the intersect() area to the sum of the areas of the Shapes' getBounds2D(). For example,

Shape s1, s2 ...
Rectangle2D r1 = s1.getBounds2D();
Rectangle2D r2 = s2.getBounds2D();
Rectangle2D r3 = new Rectangle2D.Double();
Rectangle2D.intersect(r1, r2, r3);
double overlap = area(r3) / (area(r1) + area(r2));
...
private double area(Rectangle2D r) {
    return r.getWidth() * r.getHeight();
}

您可能需要凭经验验证结果.

You may need to validate the results empirically.

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