c# - 将 3D 点投影到 2D 屏幕坐标

Question

基于 3D Programming For Windows (Charles Petzold) 第 7 章中的信息，我尝试编写辅助函数，将 Point3D 投影到包含相应屏幕坐标 (x,y) 的标准 2D 点:

public Point Point3DToScreen2D(Point3D point3D,Viewport3D viewPort )
{
    double screenX = 0d, screenY = 0d;

    // Camera is defined in XAML as:
    //        <Viewport3D.Camera>
    //             <PerspectiveCamera Position="0,0,800" LookDirection="0,0,-1" />
    //        </Viewport3D.Camera>

    PerspectiveCamera cam = viewPort.Camera as PerspectiveCamera;

    // Translate input point using camera position
    double inputX = point3D.X - cam.Position.X;
    double inputY = point3D.Y - cam.Position.Y;
    double inputZ = point3D.Z - cam.Position.Z;

    double aspectRatio = viewPort.ActualWidth / viewPort.ActualHeight;

    // Apply projection to X and Y
    screenX = inputX / (-inputZ * Math.Tan(cam.FieldOfView / 2));

    screenY = (inputY * aspectRatio) / (-inputZ * Math.Tan(cam.FieldOfView / 2));

    // Convert to screen coordinates
    screenX = screenX * viewPort.ActualWidth;

    screenY = screenY * viewPort.ActualHeight;


    // Additional, currently unused, projection scaling factors
    /*
    double xScale = 1 / Math.Tan(Math.PI * cam.FieldOfView / 360);
    double yScale = aspectRatio * xScale;

    double zFar = cam.FarPlaneDistance;
    double zNear = cam.NearPlaneDistance;

    double zScale = zFar == Double.PositiveInfinity ? -1 : zFar / (zNear - zFar);
    double zOffset = zNear * zScale;

    */

    return new Point(screenX, screenY);
}

然而，在测试中，此函数返回不正确的屏幕坐标(通过将 2D 鼠标坐标与简单的 3D 形状进行比较来检查)。由于我缺乏 3D 编程经验，我对原因感到困惑。

block 注释部分包含可能必不可少的缩放计算，但我不确定如何进行，并且本书继续介绍了使用 XAML 的 MatrixCamera。最初，我只想进行基本计算，而不管它与矩阵相比效率有多么低。

任何人都可以建议需要添加或更改的内容吗？

Answer 1

我已经使用 3DUtils 创建并成功测试了一种工作方法Codeplex 源库。

真正的工作是在 3DUtils 的 TryWorldToViewportTransform() 方法中执行的。没有它，此方法将无法工作(请参阅上面的链接)。

在 Eric Sink 的文章中也找到了非常有用的信息:Auto-Zoom .

注意。可能有更可靠/有效的方法，如果有，请将它们添加为答案。与此同时，这足以满足我的需求。

    /// <summary>
    /// Takes a 3D point and returns the corresponding 2D point (X,Y) within the viewport.  
    /// Requires the 3DUtils project available at http://www.codeplex.com/Wiki/View.aspx?ProjectName=3DTools
    /// </summary>
    /// <param name="point3D">A point in 3D space</param>
    /// <param name="viewPort">An instance of Viewport3D</param>
    /// <returns>The corresponding 2D point or null if it could not be calculated</returns>
    public Point? Point3DToScreen2D(Point3D point3D, Viewport3D viewPort)
    {
        bool bOK = false;

        // We need a Viewport3DVisual but we only have a Viewport3D.
        Viewport3DVisual vpv =VisualTreeHelper.GetParent(viewPort.Children[0]) as Viewport3DVisual;

        // Get the world to viewport transform matrix
        Matrix3D m = MathUtils.TryWorldToViewportTransform(vpv, out bOK);

        if (bOK)
        {
            // Transform the 3D point to 2D
            Point3D transformedPoint = m.Transform(point3D);

            Point screen2DPoint = new Point(transformedPoint.X, transformedPoint.Y);

            return new Nullable<Point>(screen2DPoint);
        }
        else
        {
            return null; 
        }
    }