Wpf 确定一个三维对象是否被另一个三维对象隐藏

我在Viewport3D中有一些GeometryModel3D球，其中一些球是可见的，一些球被蓝色立方体隐藏。 （尽管下面的图像是二维的，但让我们假设所有对象都是三维的）

我想确定哪些红球可以看到，哪些是隐藏的

我该怎么做

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此问题也称为，尽管您对计算被遮挡的基本体感兴趣。根据场景的条件，解决此问题的暴力方法（假设使用透视投影）是以下伪代码：

occludedSpheresCount = 0
spheres = {Set of spheres}
cubes = {Set of cubes}
normalizedCubes = {} 

# First, build the set of normalized cubes (it means, 
# take the cubes that are free in space and transform their  
# coordinates to values between [-1, -1, -1] and [1, 1, 1], they are the same
# cubes but now the coordinates are laying in that range 
# To do that, use the 

这种方法的唯一缺点是在以下情况下：

+--------------+--------------+ | -|- | | / | \ | | | | | | | \ | / | | -|- | +--------------+--------------+ or interception here | v +----------+--+--------------+ | | -|- | | /| | \ | | | | | | | | \| | / | | | -|- | +----------+--+--------------+ +--------------+--------------+ | -|- | | / | \ | | | | | | | \ | / | | -|- | +--------------+--------------+ 或 这里拦截 | v +----------+--+--------------+ | | -|- | | /| | \ | | | | | | | | \| | / | | | -|- | +----------+--+--------------+ 在这种情况下，当两个或多个多维数据集区域被拦截（可以在第一个循环中完成）时，您必须构建一组规范化多维数据集（

set{set{cube1，cube2}，set{cube3，cube4}，…}

），并且争用测试将更加复杂。但我不知道你的程序中是否允许（多维数据集拦截）

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这个算法是

O（n^2）

，因为这是一个蛮力方法，希望这能给你一个最终解决方案的提示，如果你想寻找一个更有效的更一般的解决方案，请使用类似于的东西你想知道球是否部分隐藏吗？或者你需要对它们进行二进制测试？h3nr1x-如果它只是部分隐藏，我认为它不是隐藏的。球体基本体是以对{center，radius}的形式存储还是以模型网格的形式存储（如果你以模型网格的形式存储它们，你是否存储它们的中心和半径）？立方体基本体是否存储为边界框？您使用的是正交投影还是透视投影？（我需要详细说明解决方案的信息）感谢h3nr1x-我使用MeshGeometry3Ds。如果有帮助的话，我可以存储它们的中心和半径，我正在使用PerspectiveCamera。谢谢h3nr1x，我没有成功地将您的伪代码转换为c#，WPF，所以我不知道这是否是正确的答案。

projectionMatrix = GetProjectionMatrix(perspectiveCamera)
for each cube in cubes do 
    Rect3D boundingBox = cube.Bounds()
    Rect3D normalizedBBox = projectionMatrix.transform(boundingBox)
    cubes_normalized.add(normalizedBBox)
end for

# Now search every sphere, normalize it's bounding box
# and check if it's been occluded by some normalized cube
for each sphere in spheres do
    Rect3D sphereBBox = sphere.Bounds() 
    Rect3D normalizedSphere = projectionMatrix.transform(sphereBBox)
    for each normalizedCube in normalizedCubes do
         x0 = normalizedCube.Location.X - (normalizedCube.Location.SizeX / 2)
         y0 = normalizedCube.Location.Y - (normalizedCube.Location.SizeY / 2)
         z0 = normalizedCube.Location.Z - (normalizedCube.Location.SizeZ / 2)

         xf = normalizedCube.Location.X + (normalizedCube.Location.SizeX / 2)
         yf = normalizedCube.Location.Y + (normalizedCube.Location.SizeY / 2)

         sx0 <- normalizedSphere.Location.X - (normalizedSphere.Location.SizeX / 2)
         sy0 <- normalizedSphere.Location.X - (normalizedSphere.Location.SizeY / 2)
         sz0 <- normalizedSphere.Location.X - (normalizedSphere.Location.SizeZ / 2)

         sxf <- normalizedSphere.Location.X + (normalizedSphere.Location.SizeX / 2)
         syf <- normalizedSphere.Location.X + (normalizedSphere.Location.SizeY / 2)

         # First, let's check that the normalized-sphere is behind the 
         # normalized-cube, to do that, let's compare their z-front values
         if z0 > sz0 then  
             # Now that we know that the sphere is behind the frontface of the cube 
             # lets check if it is fully contained inside the 
             # the normalized-cube, in that case, it is occluded

             if sx0 >= x0 and sxf <= xf and sy0 >= y0 and syf >= yf then
                  occludedSpheresCount++ 
                  # Here you can even avoid rendering the sphere altogether
             end if
         end if
    end for
end for

    private static Matrix3D GetProjectionMatrix(PerspectiveCamera camera, double aspectRatio)
    { 
        // This math is identical to what you find documented for
        // D3DXMatrixPerspectiveFovRH with the exception that in
        // WPF the camera's horizontal rather the vertical
        // field-of-view is specified.
        double hFoV = MathUtils.DegreesToRadians(camera.FieldOfView);
        double zn = camera.NearPlaneDistance;
        double zf = camera.FarPlaneDistance;
        double xScale = 1 / Math.Tan(hFoV / 2);
        double yScale = aspectRatio * xScale;
        double m33 = (zf == double.PositiveInfinity) ? -1 : (zf / (zn - zf));
        double m43 = zn * m33;
        return new Matrix3D(
            xScale, 0, 0, 0,
                 0, yScale, 0, 0,
                 0, 0, m33, -1,
                 0, 0, m43, 0);
    }

+--------------+--------------+ | -|- | | / | \ | | | | | | | \ | / | | -|- | +--------------+--------------+ or interception here | v +----------+--+--------------+ | | -|- | | /| | \ | | | | | | | | \| | / | | | -|- | +----------+--+--------------+