两种屏幕-世界坐标转换的性能比较

来源：互联网发布：ch341a编程器软件1.29 编辑：程序博客网时间：2024/06/03 20:19

很早之前写过一篇《D3D坐标系统下3D世界坐标映射到2D屏幕坐标的平移矩阵》，是用解方程组方式逆推出世界坐标，当然一般做法是用Raycasting方法进行计算。
Raycasting思路大致是根据屏幕坐标反投影出两个空间坐标，一般可以取及最远点，这样就组成穿过viewport的一根射线，射线和viewport相交的点就是需要的空间坐标点。
因此在表示射线ray时就可以用近点及远点两个坐标表示，一般都是用近点表示坐标，用两个点的差表示近点指向远点的方向，那么求目标坐标时只要用简单的向量计算就能得出结果。

用这两个方法都能得到正确结果，但性能有区别，实际测试，解方程组性能稍微好一点，1000万次运行大概略快5%左右。
测试代码如下：

    class Program    {        static Matrix Get2DTranslationMatrix(ViewportF viewPort, Vector2 pos, Matrix world, Matrix view, Matrix projection)        {            var screenZ = viewPort.Project(Vector3.Zero, projection, view, world);            var diff = new Vector3(pos, 0) - screenZ;            var projM = world * view * projection;            var transV = Vector3.Transform(Vector3.Zero, projM);            if (MathUtil.IsZero(transV.W))            {                transV.W = 1.0f;            }            var w = viewPort.Width;            var h = viewPort.Height;            var C1 = viewPort.X;            var C2 = viewPort.Y;            var C3 = viewPort.MaxDepth;            var C4 = viewPort.MinDepth;            var L1 = projM.M11 - projM.M14 * (transV.X / transV.W + diff.X * 2 / w);            var L2 = projM.M21 - projM.M24 * (transV.X / transV.W + diff.X * 2 / w);            var L3 = projM.M31 - projM.M34 * (transV.X / transV.W + diff.X * 2 / w);            var M1 = projM.M12 + projM.M14 * (-transV.Y / transV.W + diff.Y * 2 / h);            var M2 = projM.M22 + projM.M24 * (-transV.Y / transV.W + diff.Y * 2 / h);            var M3 = projM.M32 + projM.M34 * (-transV.Y / transV.W + diff.Y * 2 / h);            var N1 = projM.M13 - projM.M14 * (transV.Z / transV.W * (C3 - C4) + C4);            var N2 = projM.M23 - projM.M24 * (transV.Z / transV.W * (C3 - C4) + C4);            var N3 = projM.M33 - projM.M34 * (transV.Z / transV.W * (C3 - C4) + C4);            var A1 = transV.W * (transV.X / transV.W + diff.X * 2 / w) - transV.X;            var A2 = -transV.W * (-transV.Y / transV.W + diff.Y * 2 / h) - transV.Y;            var A3 = transV.W * (transV.Z / transV.W * (C3 - C4) + C4) - transV.Z;            var z = ((A3 * L1 - A1 * N1) * (M2 * L1 - L2 * M1) - (A2 * L1 - A1 * M1) * (N2 * L1 - L2 * N1)) / ((N3 * L1 - L3 * N1) * (M2 * L1 - L2 * M1) - (M3 * L1 - L3 * M1) * (N2 * L1 - L2 * N1));            var y = ((A2 * L1 - A1 * M1) - (M3 * L1 - L3 * M1) * z) / (M2 * L1 - L2 * M1);            var x = A1 / L1 - z * L3 / L1 - y * L2 / L1;            return Matrix.Translation(x, y, z);        }        static Matrix RayTest(ViewportF viewPort, Vector2 pos, Matrix world, Matrix view, Matrix projection)        {            var ray = Ray.GetPickRay((int)pos.X, (int)pos.Y, viewPort, world * view * projection);            var distance = Math.Abs(ray.Position.Z / ray.Direction.Z);            var point = ray.Position + ray.Direction * distance;            return Matrix.Translation(point);        }        static void Main(string[] args)        {            Matrix view = new Matrix(                -1f, 0f, -6.278329E-07f, 0f,                0f, 1f, 0f, 0f,                6.278329E-07f, 0f, -1f, 0f,                -0.03199686f, 0f, -5f, 1f);            Matrix projection = new Matrix(                0.9297889f, 0f, 0f, 0f,                0f, 0.7522834f, 0f, 0f,                0.01567176f, 0f, -1.000001f, -1f,                0f, 0f, -0.001000001f, 0f);            ViewportF viewPort = new ViewportF(0f, 0f, 1182f, 1461f, 0f, 1f);            Matrix world = Matrix.Scaling(0.003f);            var v = new Vector2(320, 200);            Stopwatch sw = new Stopwatch();            Console.ReadLine();            sw.Reset();            sw.Start();            for (int i = 0; i < 10000000; ++i)                Get2DTranslationMatrix(viewPort, v, world, view, projection);            sw.Stop();            var c1 = sw.ElapsedMilliseconds;            Console.WriteLine(sw.ElapsedMilliseconds);            sw.Reset();            sw.Start();            for (int i = 0; i < 10000000; ++i)                RayTest(viewPort, v, world, view, projection);            sw.Stop();            var c2 = sw.ElapsedMilliseconds;            Console.WriteLine(sw.ElapsedMilliseconds);            Console.WriteLine("{0}", c2 - c1);            Console.WriteLine("{0}", 1 - (double)c1 / c2);            Console.ReadLine();        }    }

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