Matrix3D != ProjectionMatrix SL4

Question

After a projection transform the resulting ProjectionMatrix does not equal a valid Matrix3D

Specifically the X properties are all 0.0.

Here is xaml to create two planes one with a projection.

    <Canvas x:Name="LayoutRoot" Background="White" Width="800" Height="400" MouseMove="LayoutRoot_MouseMove">
        <Canvas Background="Yellow" Width="400" Height="400" x:Name="testCanvas">
            <Canvas.Projection>
                <PlaneProjection x:Name="GProj" RotationX="-45" CenterOfRotationY="1.0" />
            </Canvas.Projection>
        </Canvas>
        <Canvas Background="Red" Width="400" Height="400" x:Name="testCanvas2" Canvas.Left="400">
        </Canvas>
        <StackPanel Orientation="Horizontal">
            <Button Content="calc" HorizontalAlignment="Center" VerticalAlignment="Center" Click="Button_Click" />
        </StackPanel>
    </Canvas>

Once the button is clicked the code copies the properties and sets the resulting matix to the second plane.

       private void Button_Click(object sender, RoutedEventArgs e)
        {
            
            Matrix3D m3dp = GProj.ProjectionMatrix;
            Matrix3DProjection matrix3DProjection = new Matrix3DProjection();
            Matrix3D matrix3D = new Matrix3D();
            matrix3D.M11 = m3dp.M11;
            matrix3D.M12 = m3dp.M12;
            matrix3D.M13 = m3dp.M13;
            matrix3D.M14 = m3dp.M14;

            matrix3D.M21 = m3dp.M21;
            matrix3D.M22 = m3dp.M22;
            matrix3D.M23 = m3dp.M23;
            matrix3D.M24 = m3dp.M24;

            matrix3D.M31 = m3dp.M31;
            matrix3D.M32 = m3dp.M32;
            matrix3D.M33 = m3dp.M33;
            matrix3D.M34 = m3dp.M34;

            matrix3D.OffsetX = m3dp.OffsetX;
            matrix3D.OffsetY = m3dp.OffsetY;
            matrix3D.OffsetZ = m3dp.OffsetZ;
            matrix3D.M44 = m3dp.M44;

            matrix3DProjection.ProjectionMatrix = matrix3D;

            testCanvas2.Projection = matrix3DProjection;

        }

Discovered when trying to perform matrix multiplications where the source matrix was the above projection.

M11, M21, M31, OffsetX is always 0.0

Answer 1

After a projection transform the resulting ProjectionMatrix does not equal a valid Matrix3D

Hi,

You are running into a wrong direction. The ProjectionMatrix is for projection only, not the matrix used to see the final result. We need to use multiple Matrix to build the result like a PlaneProjection. Actually for a given 3D objects if you view (camera viewpoint) it on different point you’ll see different results. Below is a sample of using ProjectionMatrix. Please try to adjust the final matrix to revert to whatever you need.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Net;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Animation;
using System.Windows.Shapes;
using System.Windows.Media.Media3D;
using System.Windows.Threading;

namespace SilverlightApplication17
{
    public partial class MainPage : UserControl
    {
        public MainPage()
        {
            InitializeComponent();
            this.Loaded += new RoutedEventHandler(MainPage_Loaded);
        }

        void MainPage_Loaded(object sender, RoutedEventArgs e)
        {
            DispatcherTimer dt = new DispatcherTimer();
            dt.Interval = TimeSpan.FromMilliseconds(50);
            dt.Tick += new EventHandler(dt_Tick);
            dt.Start();
        }
        double i = 0;

        void dt_Tick(object sender, EventArgs e)
        {
            i++;
            if (i >= 10000) i = 0;
            GProj.RotationX = i;
            Sync();
        }
        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;
        }


        private void Button_Click(object sender, RoutedEventArgs e)
        {
            Sync();
         

        }
        private void Sync()
        {
            Matrix3D m3dp = GProj.ProjectionMatrix;
            Matrix3DProjection matrix3DProjection = new Matrix3DProjection();
            Matrix3D matrix3D = new Matrix3D();
            matrix3D.M11 = m3dp.M11;
            matrix3D.M12 = m3dp.M12;
            matrix3D.M13 = m3dp.M13;
            matrix3D.M14 = m3dp.M14;

            matrix3D.M21 = m3dp.M21;
            matrix3D.M22 = m3dp.M22;
            matrix3D.M23 = m3dp.M23;
            matrix3D.M24 = m3dp.M24;

            matrix3D.M31 = m3dp.M31;
            matrix3D.M32 = m3dp.M32;
            matrix3D.M33 = m3dp.M33;
            matrix3D.M34 = m3dp.M34;

            matrix3D.OffsetX = m3dp.OffsetX;
            matrix3D.OffsetY = m3dp.OffsetY;
            matrix3D.OffsetZ = m3dp.OffsetZ;
            matrix3D.M44 = m3dp.M44;
            // far plane

            matrix3DProjection.ProjectionMatrix = matrix3D; //* viewport;    

            double fovY = Math.PI / 2.0;
            double translationZ = -testCanvas.ActualHeight / Math.Tan(fovY / 2.0);

            Matrix3D centerImageAtOrigin = TranslationTransform(
                     -testCanvas.ActualWidth / 2.0,
                     -testCanvas.ActualHeight / 2.0, 0);

            Matrix3D rotateAboutX = matrix3D;
            Matrix3D translateAwayFromCamera = TranslationTransform(0, 0, translationZ);
            Matrix3D perspective = PerspectiveTransformFovRH(fovY,
                    LayoutRoot.ActualWidth / LayoutRoot.ActualHeight,   // aspect ratio
                    1.0,                                                // near plane
                    1000.0);                                            // far plane
            Matrix3D viewport = ViewportTransform(LayoutRoot.ActualWidth, LayoutRoot.ActualHeight);

            Matrix3D m = centerImageAtOrigin;
            m = m * rotateAboutX;
            m = m * translateAwayFromCamera;
            m = m * perspective;
            m = m * viewport;

            testCanvas2.Projection = new Matrix3DProjection()
            {
                ProjectionMatrix = m
            };

        }
    }
}

<UserControl x:Class="SilverlightApplication17.MainPage"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d"
    d:DesignHeight="300" d:DesignWidth="400">

    <Canvas x:Name="LayoutRoot" Background="White" Width="800" Height="400" >
        <Canvas Background="Red" Width="400" Height="400" x:Name="testCanvas2" Canvas.Left="400">
        </Canvas>
        <Canvas Background="Yellow" Width="400" Height="400" x:Name="testCanvas">
            <Canvas.Projection>
                <PlaneProjection x:Name="GProj" RotationX="-85" CenterOfRotationY="1.0" />
            </Canvas.Projection>
        </Canvas>
    
        <StackPanel Orientation="Horizontal">
            <Button Content="calc" HorizontalAlignment="Center" VerticalAlignment="Center" Click="Button_Click" />
        </StackPanel>
    </Canvas>
</UserControl>

 

Answer 2

thanks for that, I will digest all that scary math.

The example works great.