.net - 如何在Matrix3D中设置这种透视变换？

Question

我有一个图像，并且有一些值可以使其成为 Silverlight 中的透视图，但无法完全弄清楚我需要在数学上做什么才能实现它。最重要的是我有一个称为“视野”(FOV) 的角度。

这是正常的图片:

例如:

X =   30°             X =   30°             X   =  30°
FOV = 30°             FOV = 60°             FOV = 120°
        

X =   60°             X =   60°               X =  60°
FOV = 30°             FOV = 60°             FOV = 120°
                       

如果能帮助我完成数学计算以在 Silverlight 中重现这些内容，我们将不胜感激。

Answer 1

我认为每个人都遇到的问题是需要随着透视变换而进行视口(viewport)移动。

试试这个:

private void ApplyProjection()
{
    double fovY = FOV * Math.PI / 180 / 2.0;
    double translationZ = -image1.ActualHeight / Math.Tan(fovY / 2.0);
    double theta = YourAngleX * Math.PI / 180.0;

    Matrix3D centerImageAtOrigin = TranslationTransform(
             -image1.ActualWidth / 2.0,
             -image1.ActualHeight / 2.0, 0);
    Matrix3D invertYAxis = CreateScaleTransform(1.0, -1.0, 1.0);
    Matrix3D rotateAboutY = RotateYTransform(theta);
    Matrix3D translateAwayFromCamera = TranslationTransform(0, 0, translationZ);
    Matrix3D perspective = PerspectiveTransformFovRH(fovY,
            image1.ActualWidth / image1.ActualHeight,   // aspect ratio
            1.0,                                                // near plane
            1000.0);                                            // far plane
    Matrix3D viewport = ViewportTransform(image1.ActualWidth, image1.ActualHeight);

    Matrix3D m = centerImageAtOrigin * invertYAxis;
    m = m * rotateAboutY;
    m = m * translateAwayFromCamera;
    m = m * perspective;
    m = m * viewport;

    Matrix3DProjection m3dProjection = new Matrix3DProjection();
    m3dProjection.ProjectionMatrix = m;

    image1.Projection = m3dProjection;
}

private Matrix3D TranslationTransform(double tx, double ty, double tz)
{
    Matrix3D m = new Matrix3D();

    m.M11 = 1.0; m.M12 = 0.0; m.M13 = 0.0; m.M14 = 0.0;
    m.M21 = 0.0; m.M22 = 1.0; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = 0.0; m.M32 = 0.0; m.M33 = 1.0; m.M34 = 0.0;
    m.OffsetX = tx; m.OffsetY = ty; m.OffsetZ = tz; m.M44 = 1.0;

    return m;
}

private Matrix3D CreateScaleTransform(double sx, double sy, double sz)
{
    Matrix3D m = new Matrix3D();

    m.M11 = sx; m.M12 = 0.0; m.M13 = 0.0; m.M14 = 0.0;
    m.M21 = 0.0; m.M22 = sy; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = 0.0; m.M32 = 0.0; m.M33 = sz; m.M34 = 0.0;
    m.OffsetX = 0.0; m.OffsetY = 0.0; m.OffsetZ = 0.0; m.M44 = 1.0;

    return m;
}

private Matrix3D RotateYTransform(double theta)
{
    double sin = Math.Sin(theta);
    double cos = Math.Cos(theta);

    Matrix3D m = new Matrix3D();

    m.M11 = cos; m.M12 = 0.0; m.M13 = -sin; m.M14 = 0.0;
    m.M21 = 0.0; m.M22 = 1.0; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = sin; m.M32 = 0.0; m.M33 = cos; m.M34 = 0.0;
    m.OffsetX = 0.0; m.OffsetY = 0.0; m.OffsetZ = 0.0; m.M44 = 1.0;

    return m;
}

private Matrix3D RotateZTransform(double theta)
{
    double cos = Math.Cos(theta);
    double sin = Math.Sin(theta);

    Matrix3D m = new Matrix3D();
    m.M11 = cos; m.M12 = sin; m.M13 = 0.0; m.M14 = 0.0;
    m.M21 = -sin; m.M22 = cos; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = 0.0; m.M32 = 0.0; m.M33 = 1.0; m.M34 = 0.0;
    m.OffsetX = 0.0; m.OffsetY = 0.0; m.OffsetZ = 0.0; m.M44 = 1.0;
    return m;
}

private Matrix3D PerspectiveTransformFovRH(double fieldOfViewY, double aspectRatio, double zNearPlane, double zFarPlane)
{
    double height = 1.0 / Math.Tan(fieldOfViewY / 2.0);
    double width = height / aspectRatio;
    double d = zNearPlane - zFarPlane;

    Matrix3D m = new Matrix3D();
    m.M11 = width; m.M12 = 0; m.M13 = 0; m.M14 = 0;
    m.M21 = 0; m.M22 = height; m.M23 = 0; m.M24 = 0;
    m.M31 = 0; m.M32 = 0; m.M33 = zFarPlane / d; m.M34 = -1;
    m.OffsetX = 0; m.OffsetY = 0; m.OffsetZ = zNearPlane * zFarPlane / d; m.M44 = 0;

    return m;
}

private Matrix3D ViewportTransform(double width, double height)
{
    Matrix3D m = new Matrix3D();

    m.M11 = width / 2.0; m.M12 = 0.0; m.M13 = 0.0; m.M14 = 0.0;
    m.M21 = 0.0; m.M22 = -height / 2.0; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = 0.0; m.M32 = 0.0; m.M33 = 1.0; m.M34 = 0.0;
    m.OffsetX = width / 2.0; m.OffsetY = height / 2.0; m.OffsetZ = 0.0; m.M44 = 1.0;

    return m;
}

这将创建适当的视角转换并与 PowerPoint 生成的内容相匹配。

此代码改编自MSDN .