private Point3D[,] Redraw(string nodename)
{
var data = new Point3D[model.Rows + 1, model.Columns + 1];
var dataOriginal = new Point4D[model.Rows + 1, model.Columns + 1];
MathNet.Numerics.Complex32 W;
for (int i = 0; i <= model.Rows; i++)
for (int j = 0; j <= model.Columns; j++)
{
W = sol1.WfromIndexes[new Tuple<int, int>(i, j)];
foreach (var node in sol1.Voltages[W])
{
if (node.Key == nodename)
{
data[i, j] = new Point3D(W.Real,
W.Imaginary,
//node.Value.Magnitude);
Math.Log10(node.Value.Magnitude));
dataOriginal[i, j] = new Point4D(W.Real, W.Imaginary,
node.Value.Magnitude, node.Value.Phase);
}
}
}
surface.OriginalData = dataOriginal;
model.Data = data;
model.UpdateModel(false);
return data;
}
public NewtonVector4(Point4D vector)
{
this.Vector[0] = (float)vector.X;
this.Vector[1] = (float)vector.Y;
this.Vector[2] = (float)vector.Z;
this.Vector[3] = (float)vector.W;
}
public NewtonVector4(Point4D pVector)
{
NWVector4[ 0 ] = (float)pVector.X;
NWVector4[ 1 ] = (float)pVector.Y;
NWVector4[ 2 ] = (float)pVector.Z;
NWVector4[ 3 ] = (float)pVector.W;
}
public object m_UserData; // user data passed to the collision geometry at creation time
internal UserMeshCollisionRayHitDesc(Newton.NewtonUserMeshCollisionRayHitDesc pRayHitDesc)
{
m_NormalOut = new NewtonVector4(pRayHitDesc.m_NormalOut).ToDirectX();
m_P0 = new NewtonVector4(pRayHitDesc.m_P0).ToDirectX();
m_P1 = new NewtonVector4(pRayHitDesc.m_P1).ToDirectX();
m_UserData = CHashTables.BodyUserData[pRayHitDesc.m_UserData];
m_UserIdOut = pRayHitDesc.m_UserIdOut;
}
public Point4D ToDirectX()
{
Point4D aDXVecor = new Point4D();
aDXVecor.X = NWVector4[0];
aDXVecor.Y = NWVector4[1];
aDXVecor.Z = NWVector4[2];
aDXVecor.W = NWVector4[3];
return aDXVecor;
}
// Displays the values of the variables
public void ShowVars()
{
Point4D p1 = new Point4D(10, 5, 1, 4);
Point4D p2 = new Point4D(15, 40, 60, 75);
Matrix3D m1 = new Matrix3D(10,10,10,0,20,20,20,0,30,30,30,0,5,10,15,1);
// Displaying values in Text objects
txtPoint1.Text = p1.ToString();
txtPoint2.Text = p2.ToString();
txtMatrix1.Text = m1.ToString();
}
public CBody m_PolySoupBody; // pointer to the rigid body owner of this collision tree
internal UserMeshCollisionCollideDesc(Newton.NewtonUserMeshCollisionCollideDesc pDesc)
{
m_BoxP0 = new NewtonVector4(pDesc.m_BoxP0).ToDirectX();
m_BoxP1 = new NewtonVector4(pDesc.m_BoxP1).ToDirectX();
m_UserData = pDesc.m_UserData;
m_FaceCount = pDesc.m_FaceCount;
m_Vertex = pDesc.m_Vertex;
m_VertexStrideInBytes = pDesc.m_VertexStrideInBytes;
m_UserAttribute = pDesc.m_UserAttribute;
m_FaceIndexCount = pDesc.m_FaceIndexCount;
m_FaceVertexIndex = pDesc.m_FaceVertexIndex;
m_ObjBody = (CBody)CHashTables.Body[pDesc.m_ObjBody];
m_PolySoupBody = (CBody)CHashTables.Body[pDesc.m_PolySoupBody];
}
/// <summary>
/// Gets the billboard positions with the current screen transform.
/// </summary>
/// <param name="billboards">The billboards.</param>
/// <param name="offset">The offset.</param>
/// <returns>The positions.</returns>
public Point3DCollection GetPositions(IList<Billboard> billboards, Vector offset)
{
var positions = new Point3DCollection(billboards.Count * 4);
foreach (var bb in billboards)
{
Point4D screenPoint;
if (!bb.WorldDepthOffset.Equals(0))
{
var viewPoint = (Point4D)bb.Position * this.visualToProjection;
screenPoint = new Point4D(viewPoint.X, viewPoint.Y, viewPoint.Z + bb.WorldDepthOffset, viewPoint.W) * this.projectionToScreen;
}
else
{
screenPoint = (Point4D)bb.Position * this.visualToScreen;
}
double spw = screenPoint.W;
double spx = screenPoint.X;
double spy = screenPoint.Y;
double spz = screenPoint.Z - (bb.DepthOffset * spw);
// Convert bottom-left corner to visual space
var p = new Point4D(spx + ((bb.Left + offset.X) * spw), spy + ((bb.Bottom + offset.Y) * spw), spz, spw) * this.screenToVisual;
double wi = 1 / p.W;
positions.Add(new Point3D(p.X * wi, p.Y * wi, p.Z * wi));
// Convert bottom-right corner to visual space
p = new Point4D(spx + ((bb.Right + offset.X) * spw), spy + ((bb.Bottom + offset.Y) * spw), spz, spw) * this.screenToVisual;
wi = 1 / p.W;
positions.Add(new Point3D(p.X * wi, p.Y * wi, p.Z * wi));
// Convert top-right corner to visual space
p = new Point4D(spx + ((bb.Right + offset.X) * spw), spy + ((bb.Top + offset.Y) * spw), spz, spw) * this.screenToVisual;
wi = 1 / p.W;
positions.Add(new Point3D(p.X * wi, p.Y * wi, p.Z * wi));
// Convert top-left corner to visual space
p = new Point4D(spx + ((bb.Left + offset.X) * spw), spy + ((bb.Top + offset.Y) * spw), spz, spw) * this.screenToVisual;
wi = 1 / p.W;
positions.Add(new Point3D(p.X * wi, p.Y * wi, p.Z * wi));
}
positions.Freeze();
return positions;
}
/// <summary>
/// ConvertTo - Attempt to convert an instance of Point4D to the given type
/// </summary>
/// <returns>
/// The object which was constructoed.
/// </returns>
/// <exception cref="NotSupportedException">
/// A NotSupportedException is thrown if "value" is null or not an instance of Point4D,
/// or if the destinationType isn't one of the valid destination types.
/// </exception>
/// <param name="context"> The ITypeDescriptorContext for this call. </param>
/// <param name="culture"> The CultureInfo which is respected when converting. </param>
/// <param name="value"> The object to convert to an instance of "destinationType". </param>
/// <param name="destinationType"> The type to which this will convert the Point4D instance. </param>
public override object ConvertTo(ITypeDescriptorContext context, CultureInfo culture, object value, Type destinationType)
{
if (destinationType != null && value is Point4D)
{
Point4D instance = (Point4D)value;
if (destinationType == typeof(string))
{
// Delegate to the formatting/culture-aware ConvertToString method.
#pragma warning suppress 6506 // instance is obviously not null
return(instance.ConvertToString(null, culture));
}
}
// Pass unhandled cases to base class (which will throw exceptions for null value or destinationType.)
return(base.ConvertTo(context, culture, value, destinationType));
}
internal Point WorldToViewport(Point4D point)
{
double aspectRatio = M3DUtil.GetAspectRatio(Viewport.Size);
Camera camera = Camera;
if (camera != null)
{
Matrix3D viewProjMatrix = camera.GetViewMatrix() * camera.GetProjectionMatrix(aspectRatio);
point *= viewProjMatrix;
Point point2D = new Point(point.X / point.W, point.Y / point.W);
point2D *= M3DUtil.GetHomogeneousToViewportTransform(Viewport);
return(point2D);
}
else
{
return(new Point(0, 0));
}
}
/// <summary>
/// Parse - returns an instance converted from the provided string using
/// the culture "en-US"
/// <param name="source"> string with Point4D data </param>
/// </summary>
public static Point4D Parse(string source)
{
IFormatProvider formatProvider = System.Windows.Markup.TypeConverterHelper.InvariantEnglishUS;
TokenizerHelper th = new TokenizerHelper(source, formatProvider);
Point4D value;
String firstToken = th.NextTokenRequired();
value = new Point4D(
Convert.ToDouble(firstToken, formatProvider),
Convert.ToDouble(th.NextTokenRequired(), formatProvider),
Convert.ToDouble(th.NextTokenRequired(), formatProvider),
Convert.ToDouble(th.NextTokenRequired(), formatProvider));
// There should be no more tokens in this string.
th.LastTokenRequired();
return(value);
}
/// <summary>
/// Gets the billboard positions with the current screen transform.
/// </summary>
/// <returns>The positions.</returns>
public Point3DCollection GetPositions(IList<Billboard> billboards)
{
var positions = new Point3DCollection(billboards.Count * 4);
foreach (var bb in billboards)
{
var screenPoint = (Point4D)bb.Position * this.visualToScreen;
double spx = screenPoint.X;
double spy = screenPoint.Y;
double spz = screenPoint.Z;
double spw = screenPoint.W;
if (!bb.DepthOffset.Equals(0))
{
spz -= bb.DepthOffset * spw;
}
var p0 = new Point4D(spx, spy, spz, spw) * this.screenToVisual;
double pwinverse = 1 / p0.W;
var p1 = new Point4D(spx + bb.Left * spw, spy + bb.Bottom * spw, spz, spw) * this.screenToVisual;
positions.Add(new Point3D(p1.X * pwinverse, p1.Y * pwinverse, p1.Z * pwinverse));
var p2 = new Point4D(spx + bb.Right * spw, spy + bb.Bottom * spw, spz, spw) * this.screenToVisual;
positions.Add(new Point3D(p2.X * pwinverse, p2.Y * pwinverse, p2.Z * pwinverse));
var p3 = new Point4D(spx + bb.Right * spw, spy + bb.Top * spw, spz, spw) * this.screenToVisual;
positions.Add(new Point3D(p3.X * pwinverse, p3.Y * pwinverse, p3.Z * pwinverse));
var p4 = new Point4D(spx + bb.Left * spw, spy + bb.Top * spw, spz, spw) * this.screenToVisual;
positions.Add(new Point3D(p4.X * pwinverse, p4.Y * pwinverse, p4.Z * pwinverse));
}
positions.Freeze();
return positions;
}
// updates the matrices and plane equation and sends it to the pixel shader.</summary>
private void _updateMatricesAndShaderValues() {
// Creating the worldViewProj matrix corresponding to the current plane transformation
_worldViewProj = PlaneTransformation * _viewProjMatrix;
if (RecenterViewport) {
Point3D transformedCenter = _worldViewProj.Transform(new Point3D(0, 0, 0));
ViewportOffset = new Point(transformedCenter.X, transformedCenter.Y);
_hitTestingTransform.ViewportOffset = ViewportOffset;
}
_worldViewProjI = _worldViewProj;
// and its inversed matrix
_worldViewProjI.Invert();
_hitTestingTransform.PlaneTransformation = _worldViewProj;
_hitTestingTransform.InverseTransformation = _worldViewProjI;
// Calculate the 3 coordinates of the plane after transformation
var rawTopLeft = _worldViewProj.Transform(new Point3D(-1, 1, 0));
var rawTopRight = _worldViewProj.Transform(new Point3D(1, 1, 0));
var rawBottomLeft = _worldViewProj.Transform(new Point3D(-1, -1, 0));
// compute the normal of the plane
var planeNormal = Vector3D.CrossProduct((rawTopRight - rawTopLeft), (rawBottomLeft - rawTopLeft));
planeNormal.Normalize();
PlaneNormal = planeNormal;
_hitTestingTransform.PlaneNormal = planeNormal;
// and its distance from the origin
this.PlaneDistance = -Vector3D.DotProduct(planeNormal, new Vector3D(rawTopLeft.X, rawTopLeft.Y, rawTopLeft.Z));
_hitTestingTransform.PlaneDistance = this.PlaneDistance;
// Pass it to the pixel shader
M1 = new Point4D(_worldViewProjI.M11, _worldViewProjI.M12, _worldViewProjI.M13, _worldViewProjI.M14);
M2 = new Point4D(_worldViewProjI.M21, _worldViewProjI.M22, _worldViewProjI.M23, _worldViewProjI.M24);
M3 = new Point4D(_worldViewProjI.M31, _worldViewProjI.M32, _worldViewProjI.M33, _worldViewProjI.M34);
M4 = new Point4D(_worldViewProjI.OffsetX, _worldViewProjI.OffsetY, _worldViewProjI.OffsetZ, _worldViewProjI.M44);
}
/// <summary>
/// Equals - compares this Point4D with the passed in object. In this equality
/// Double.NaN is equal to itself, unlike in numeric equality.
/// Note that double values can acquire error when operated upon, such that
/// an exact comparison between two values which
/// are logically equal may fail.
/// </summary>
/// <returns>
/// bool - true if "value" is equal to "this".
/// </returns>
/// <param name='value'>The Point4D to compare to "this"</param>
public bool Equals(Point4D value)
{
return(Point4D.Equals(this, value));
}
internal override RayHitTestParameters RayFromViewportPoint(Point p, Size viewSize, Rect3D boundingRect, out double distanceAdjustment)
{
//
// Compute rayParameters
//
// Find the point on the projection plane in post-projective space where
// the viewport maps to a 2x2 square from (-1,1)-(1,-1).
Point np = M3DUtil.GetNormalizedPoint(p, viewSize);
//
// So (conceptually) the user clicked on the point (np.X,
// np.Y, 0) in post-projection clipping space and the ray
// extends in the direction (0, 0, 1) because our ray
// after projection looks down the positive z axis. We
// need to convert this ray and direction back to world
// space.
Matrix3D worldToCamera = GetViewMatrix() * ProjectionMatrix;
Matrix3D cameraToWorld = worldToCamera;
if (!cameraToWorld.HasInverse)
{
//
// NTRAID#Longhorn-1180933-2004/07/30-danwo - Need to handle singular matrix cameras
throw new NotSupportedException(SR.Get(SRID.HitTest_Singular));
}
cameraToWorld.Invert();
Point4D origin4D = new Point4D(np.X,np.Y,0,1) * cameraToWorld;
Point3D origin = new Point3D( origin4D.X/origin4D.W,
origin4D.Y/origin4D.W,
origin4D.Z/origin4D.W );
// To transform the direction we use the Jacobian of
// cameraToWorld at the point np.X,np.Y,0 that we just
// transformed.
//
// The Jacobian of the homogeneous matrix M is a 3x3 matrix.
//
// Let x be the point we are computing the Jacobian at, and y be the
// result of transforming x by M, i.e.
// (wy w) = (x 1) M
// Where (wy w) is the homogeneous point representing y with w as its homogeneous coordinate
// And (x 1) is the homogeneous point representing x with 1 as its homogeneous coordinate
//
// Then the i,j component of the Jacobian (at x) is
// (M_ij - M_i4 y_j) / w
//
// Since we're only concerned with the direction of the
// transformed vector and not its magnitude, we can scale
// this matrix by a POSITIVE factor. The computation
// below computes the Jacobian scaled by 1/w and then
// after we normalize the final vector we flip it around
// if w is negative.
//
// To transform a vector we just right multiply it by this Jacobian matrix.
//
// Compute the Jacobian at np.X,np.Y,0 ignoring the constant factor of w.
// Here's the pattern
//
// double Jij = cameraToWorld.Mij - cameraToWorld.Mi4 * origin.j
//
// but we only need J31,J32,&J33 because we're only
// transforming the vector 0,0,1
double J31 = cameraToWorld.M31 - cameraToWorld.M34 * origin.X;
double J32 = cameraToWorld.M32 - cameraToWorld.M34 * origin.Y;
double J33 = cameraToWorld.M33 - cameraToWorld.M34 * origin.Z;
// Then multiply that matrix by (0, 0, 1) which is
// the direction of the ray in post-projection space.
Vector3D direction = new Vector3D( J31, J32, J33 );
direction.Normalize();
// We multiplied by the Jacobian times W, so we need to
// account for whether that flipped our result or not.
if (origin4D.W < 0)
{
direction = -direction;
}
RayHitTestParameters rayParameters = new RayHitTestParameters(origin, direction);
//
// Compute HitTestProjectionMatrix
//
// The viewportMatrix will take normalized clip space into
// viewport coordinates, with an additional 2D translation
// to put the ray at the origin.
Matrix3D viewportMatrix = new Matrix3D();
viewportMatrix.TranslatePrepend(new Vector3D(-p.X,viewSize.Height-p.Y,0));
viewportMatrix.ScalePrepend(new Vector3D(viewSize.Width/2,-viewSize.Height/2,1));
viewportMatrix.TranslatePrepend(new Vector3D(1,1,0));
// `First world-to-camera, then camera's projection, then normalized clip space to viewport.
rayParameters.HitTestProjectionMatrix =
worldToCamera *
viewportMatrix;
//
// MatrixCamera does not allow for Near/Far plane adjustment, so
// the distanceAdjustment remains 0.
//
distanceAdjustment = 0.0;
return rayParameters;
}
/// <summary>
/// Point4D * Matrix3D multiplication.
/// </summary>
/// <param name="point">Point being transformed.</param>
/// <param name="matrix">Transformation matrix applied to the point.</param>
/// <returns>Result of the transformation matrix applied to the point.</returns>
public static Point4D Multiply(Point4D point, Matrix3D matrix)
{
return matrix.Transform(point);
}
/// <summary>
/// Compares two Point4D instances for object equality. In this equality
/// Double.NaN is equal to itself, unlike in numeric equality.
/// Note that double values can acquire error when operated upon, such that
/// an exact comparison between two values which
/// are logically equal may fail.
/// </summary>
/// <returns>
/// bool - true if the two Point4D instances are exactly equal, false otherwise
/// </returns>
/// <param name='point1'>The first Point4D to compare</param>
/// <param name='point2'>The second Point4D to compare</param>
public static bool Equals (Point4D point1, Point4D point2)
{
return point1.X.Equals(point2.X) &&
point1.Y.Equals(point2.Y) &&
point1.Z.Equals(point2.Z) &&
point1.W.Equals(point2.W);
}
/// <summary>
/// Parse - returns an instance converted from the provided string using
/// the culture "en-US"
/// <param name="source"> string with Point4D data </param>
/// </summary>
public static Point4D Parse(string source)
{
IFormatProvider formatProvider = System.Windows.Markup.TypeConverterHelper.InvariantEnglishUS;
TokenizerHelper th = new TokenizerHelper(source, formatProvider);
Point4D value;
String firstToken = th.NextTokenRequired();
value = new Point4D(
Convert.ToDouble(firstToken, formatProvider),
Convert.ToDouble(th.NextTokenRequired(), formatProvider),
Convert.ToDouble(th.NextTokenRequired(), formatProvider),
Convert.ToDouble(th.NextTokenRequired(), formatProvider));
// There should be no more tokens in this string.
th.LastTokenRequired();
return value;
}
/// <summary>
/// Transforms the given point by the current matrix.
/// </summary>
/// <param name="point">Point to transform.</param>
/// <returns>Transformed point.</returns>
public Point4D Transform(Point4D point)
{
MultiplyPoint(ref point);
return point;
}
/// <summary>
/// Helper function to transform a Kinect SkeletonPoint using a
/// transform matrix.
/// </summary>
/// <param name="transform">The transform to use</param>
/// <param name="skeletonPoint">The skeleton point to be transformed</param>
/// <returns>the transformed skeleton point</returns>
public static SkeletonPoint TransformSkeletonPoint(Matrix3D transform, SkeletonPoint skeletonPoint)
{
var point = new Point4D(skeletonPoint.X, skeletonPoint.Y, skeletonPoint.Z, 1.0);
point = transform.Transform(point);
return new SkeletonPoint { X = (float)point.X, Y = (float)point.Y, Z = (float)point.Z };
}
public void set_entry_needle(Joints joint)
{
double central_angle = get_central_angle();
Optimizer optimizer = new Optimizer();
Point4D target = new Point4D(entry_point.X, entry_point.Y, entry_point.Z, central_angle);
Console.Write("\noTarget entry: {0}, {1}, {2}, {3}", entry_point.X, entry_point.Y, entry_point.Z, central_angle);
optimizer.point_target = target;
optimizer.x = new double[] { joint.UpperBevel, joint.LowerBevel, joint.Elbow, joint.twist };
Joints optimized = optimizer.minimize_angle();
needle_entry.kinematics.joint.UpperBevel = optimized.UpperBevel;
needle_entry.kinematics.joint.LowerBevel = optimized.LowerBevel;
needle_entry.kinematics.joint.Elbow = optimized.Elbow;
needle_entry.kinematics.joint.twist = optimized.twist;
needle_entry.update_needle();
// setup needle_mid
needle_mid.kinematics.joint.UpperBevel = needle_entry.kinematics.joint.UpperBevel;
needle_mid.kinematics.joint.LowerBevel = needle_entry.kinematics.joint.LowerBevel;
needle_mid.kinematics.joint.Elbow = needle_entry.kinematics.joint.Elbow;
needle_mid.kinematics.joint.twist = needle_entry.kinematics.joint.twist;
needle_mid.update_needle();
}
/// <summary>
/// Transforms the given points by the current matrix.
/// </summary>
/// <param name="points">Points to transform.</param>
public void Transform(Point4D[] points)
{
if (points != null)
{
for(int i = 0; i < points.Length; i++)
{
MultiplyPoint(ref points[i]);
}
}
}
// needle center for the needle frame and a point
public Joints update_trajectory(Joints joint)
{
// not used
double central_angle = get_central_angle();
Optimizer optimizer = new Optimizer();
Point4D target = new Point4D(entry_point.X, entry_point.Y, entry_point.Z, central_angle);
optimizer.point_target = target;
optimizer.x = new double[] { joint.UpperBevel, joint.LowerBevel, joint.Elbow, joint.twist };
Joints optimized = optimizer.minimize_angle();
return optimized;
//Vector3D projected_exit_point = project_point(exit_point, needle_normal, needle_point);
//Matrix3D head = calculate_needle_tip(entry_point, projected_exit_point, needle_normal);
}
public Point4D Transform(Point4D point)
{
return(default(Point4D));
}
/// <summary>
/// Addition.
/// </summary>
/// <param name="point1">First point being added.</param>
/// <param name="point2">Second point being added.</param>
/// <returns>Result of addition.</returns>
public static Point4D Add(Point4D point1, Point4D point2)
{
return new Point4D(point1._x + point2._x,
point1._y + point2._y,
point1._z + point2._z,
point1._w + point2._w);
}
// Multiplies the given Point4D by this matrix.
//
// The point is modified in place for performance.
//
internal void MultiplyPoint(ref Point4D point)
{
if (IsDistinguishedIdentity)
return;
double x = point.X;
double y = point.Y;
double z = point.Z;
double w = point.W;
point.X = x*_m11 + y*_m21 + z*_m31 + w*_offsetX;
point.Y = x*_m12 + y*_m22 + z*_m32 + w*_offsetY;
point.Z = x*_m13 + y*_m23 + z*_m33 + w*_offsetZ;
point.W = x*_m14 + y*_m24 + z*_m34 + w*_m44;
}
internal override RayHitTestParameters RayFromViewportPoint(Point p, Size viewSize, Rect3D boundingRect, out double distanceAdjustment)
{
//
// Compute rayParameters
//
// Find the point on the projection plane in post-projective space where
// the viewport maps to a 2x2 square from (-1,1)-(1,-1).
Point np = M3DUtil.GetNormalizedPoint(p, viewSize);
// This ray is consistent with a left-handed camera
// MatrixCamera should be right-handed and should be updated to be so.
// So (conceptually) the user clicked on the point (np.X,
// np.Y, 0) in post-projection clipping space and the ray
// extends in the direction (0, 0, 1) because our ray
// after projection looks down the positive z axis. We
// need to convert this ray and direction back to world
// space.
Matrix3D worldToCamera = GetViewMatrix() * ProjectionMatrix;
Matrix3D cameraToWorld = worldToCamera;
if (!cameraToWorld.HasInverse)
{
// When the following issue is addressed we should
// investigate if the custom code paths in Orthographic and PerspectiveCamera
// are worth keeping. They may not be buying us anything aside from handling
// singular matrices.
// Need to handle singular matrix cameras
throw new NotSupportedException(SR.Get(SRID.HitTest_Singular));
}
cameraToWorld.Invert();
Point4D origin4D = new Point4D(np.X, np.Y, 0, 1) * cameraToWorld;
Point3D origin = new Point3D(origin4D.X / origin4D.W,
origin4D.Y / origin4D.W,
origin4D.Z / origin4D.W);
// To transform the direction we use the Jacobian of
// cameraToWorld at the point np.X,np.Y,0 that we just
// transformed.
//
// The Jacobian of the homogeneous matrix M is a 3x3 matrix.
//
// Let x be the point we are computing the Jacobian at, and y be the
// result of transforming x by M, i.e.
// (wy w) = (x 1) M
// Where (wy w) is the homogeneous point representing y with w as its homogeneous coordinate
// And (x 1) is the homogeneous point representing x with 1 as its homogeneous coordinate
//
// Then the i,j component of the Jacobian (at x) is
// (M_ij - M_i4 y_j) / w
//
// Since we're only concerned with the direction of the
// transformed vector and not its magnitude, we can scale
// this matrix by a POSITIVE factor. The computation
// below computes the Jacobian scaled by 1/w and then
// after we normalize the final vector we flip it around
// if w is negative.
//
// To transform a vector we just right multiply it by this Jacobian matrix.
//
// Compute the Jacobian at np.X,np.Y,0 ignoring the constant factor of w.
// Here's the pattern
//
// double Jij = cameraToWorld.Mij - cameraToWorld.Mi4 * origin.j
//
// but we only need J31,J32,&J33 because we're only
// transforming the vector 0,0,1
double J31 = cameraToWorld.M31 - cameraToWorld.M34 * origin.X;
double J32 = cameraToWorld.M32 - cameraToWorld.M34 * origin.Y;
double J33 = cameraToWorld.M33 - cameraToWorld.M34 * origin.Z;
// Then multiply that matrix by (0, 0, 1) which is
// the direction of the ray in post-projection space.
Vector3D direction = new Vector3D(J31, J32, J33);
direction.Normalize();
// We multiplied by the Jacobian times W, so we need to
// account for whether that flipped our result or not.
if (origin4D.W < 0)
{
direction = -direction;
}
RayHitTestParameters rayParameters = new RayHitTestParameters(origin, direction);
//
// Compute HitTestProjectionMatrix
//
// The viewportMatrix will take normalized clip space into
// viewport coordinates, with an additional 2D translation
// to put the ray at the origin.
Matrix3D viewportMatrix = new Matrix3D();
viewportMatrix.TranslatePrepend(new Vector3D(-p.X, viewSize.Height - p.Y, 0));
viewportMatrix.ScalePrepend(new Vector3D(viewSize.Width / 2, -viewSize.Height / 2, 1));
viewportMatrix.TranslatePrepend(new Vector3D(1, 1, 0));
// `First world-to-camera, then camera's projection, then normalized clip space to viewport.
rayParameters.HitTestProjectionMatrix =
worldToCamera *
viewportMatrix;
//
// MatrixCamera does not allow for Near/Far plane adjustment, so
// the distanceAdjustment remains 0.
//
distanceAdjustment = 0.0;
return(rayParameters);
}
internal Point WorldToViewport(Point4D point)
{
double aspectRatio = M3DUtil.GetAspectRatio(Viewport.Size);
Camera camera = Camera;
if (camera != null)
{
Matrix3D viewProjMatrix = camera.GetViewMatrix() * camera.GetProjectionMatrix(aspectRatio);
point *= viewProjMatrix;
Point point2D = new Point(point.X/point.W, point.Y/point.W);
point2D *= M3DUtil.GetHomogeneousToViewportTransform(Viewport);
return point2D;
}
else
{
return new Point(0,0);
}
}
/// <summary>
/// Transforms the given list of points.
/// </summary>
/// <param name="points">List of points.</param>
public void Transform(Point4D[] points)
{
Value.Transform(points);
}
public void Transform(Point4D[] points)
{
}
/// <summary>
/// Transforms the given point.
/// </summary>
/// <param name="point">Point to transform.</param>
/// <returns>Transformed point.</returns>
public Point4D Transform(Point4D point)
{
return Value.Transform(point);
}
/// <summary>
/// Equals - compares this Point4D with the passed in object. In this equality
/// Double.NaN is equal to itself, unlike in numeric equality.
/// Note that double values can acquire error when operated upon, such that
/// an exact comparison between two values which
/// are logically equal may fail.
/// </summary>
/// <returns>
/// bool - true if "value" is equal to "this".
/// </returns>
/// <param name='value'>The Point4D to compare to "this"</param>
public bool Equals(Point4D value)
{
return Point4D.Equals(this, value);
}
/// <summary>
/// Creates the positions for the specified points.
/// </summary>
/// <param name="points">
/// The points.
/// </param>
/// <param name="size">
/// The size of the points.
/// </param>
/// <param name="depthOffset">
/// The depth offset. A positive number (e.g. 0.0001) moves the point towards the camera.
/// </param>
/// <returns>
/// The positions collection.
/// </returns>
public Point3DCollection CreatePositions(IList<Point3D> points, double size = 1.0, double depthOffset = 0.0)
{
double halfSize = size / 2.0;
int numPoints = points.Count;
var outline = new[]
{
new Vector(-halfSize, halfSize), new Vector(-halfSize, -halfSize), new Vector(halfSize, halfSize),
new Vector(halfSize, -halfSize)
};
var positions = new Point3DCollection(numPoints * 4);
for (int i = 0; i < numPoints; i++)
{
var screenPoint = (Point4D)points[i] * this.visualToScreen;
double spx = screenPoint.X;
double spy = screenPoint.Y;
double spz = screenPoint.Z;
double spw = screenPoint.W;
if (!depthOffset.Equals(0))
{
spz -= depthOffset * spw;
}
var p0 = new Point4D(spx, spy, spz, spw) * this.screenToVisual;
double pwinverse = 1 / p0.W;
foreach (var v in outline)
{
var p = new Point4D(spx + v.X * spw, spy + v.Y * spw, spz, spw) * this.screenToVisual;
positions.Add(new Point3D(p.X * pwinverse, p.Y * pwinverse, p.Z * pwinverse));
}
}
positions.Freeze();
return positions;
}
/// <summary>
/// Transforms the given point by the current matrix.
/// </summary>
/// <param name="point">Point to transform.</param>
/// <returns>Transformed point.</returns>
public Point4D Transform(Point4D point)
{
MultiplyPoint(ref point);
return(point);
}
/// <summary>
/// Point4D * Matrix3D multiplication.
/// </summary>
/// <param name="point">Point being transformed.</param>
/// <param name="matrix">Transformation matrix applied to the point.</param>
/// <returns>Result of the transformation matrix applied to the point.</returns>
public static Point4D Multiply(Point4D point, Matrix3D matrix)
{
return(matrix.Transform(point));
}
/// <summary>
/// Gets the billboard positions with the current screen transform.
/// </summary>
/// <param name="billboards">The billboards.</param>
/// <param name="offset">The offset.</param>
/// <param name="pinWidth">Width of the pins.</param>
/// <returns>The mesh vertices.</returns>
public Point3DCollection GetPinPositions(IList<Billboard> billboards, Vector offset, double pinWidth)
{
var pinStart = new Point(0, 0);
var pinEnd = pinStart + (offset * (1 + (2 * pinWidth / offset.Length)));
var pinNormal = new Vector(pinEnd.Y, -pinEnd.X);
pinNormal.Normalize();
pinNormal *= pinWidth * 0.5;
var pinPoints = new Point[4];
pinPoints[0] = new Point(0, 0) + (pinNormal * 0.5);
pinPoints[1] = new Point(0, 0) - (pinNormal * 0.5);
pinPoints[2] = pinEnd - pinNormal;
pinPoints[3] = pinEnd + pinNormal;
var positions = new Point3DCollection(billboards.Count * 4);
foreach (var bb in billboards)
{
Point4D screenPoint;
if (!bb.WorldDepthOffset.Equals(0))
{
var viewPoint = (Point4D)bb.Position * this.visualToProjection;
screenPoint = new Point4D(viewPoint.X, viewPoint.Y, viewPoint.Z + bb.WorldDepthOffset, viewPoint.W) * this.projectionToScreen;
}
else
{
screenPoint = (Point4D)bb.Position * this.visualToScreen;
}
double spw = screenPoint.W;
double spx = screenPoint.X;
double spy = screenPoint.Y;
double spz = screenPoint.Z - ((bb.DepthOffset - 1e-5) * spw);
foreach (var pinPoint in pinPoints)
{
var p = new Point4D(spx + (pinPoint.X * spw), spy + (pinPoint.Y * spw), spz, spw) * this.screenToVisual;
double wi = 1 / p.W;
positions.Add(new Point3D(p.X * wi, p.Y * wi, p.Z * wi));
}
}
positions.Freeze();
return positions;
}
/// <summary>
/// Subtraction.
/// </summary>
/// <param name="point1">Point from which we are subtracting the second point.</param>
/// <param name="point2">Point being subtracted.</param>
/// <returns>Vector between the two points.</returns>
public static Point4D Subtract(Point4D point1, Point4D point2)
{
return new Point4D(point1._x - point2._x,
point1._y - point2._y,
point1._z - point2._z,
point1._w - point2._w);
}
// This method performs the Point operations
public void PerformOperation(object sender, RoutedEventArgs e)
{
RadioButton li = (sender as RadioButton);
// Strings used to display the results
String syntaxString, resultType, operationString;
// The local variables point1, point2, vector2, etc are defined in each
// case block for readability reasons. Each variable is contained within
// the scope of each case statement.
switch (li.Name)
{ //begin switch
case "rb1":
{
// Converts a String to a Point using a PointConverter
// Returns a Point.
PointConverter pConverter = new PointConverter();
Point pointResult = new Point();
string string1 = "10,20";
pointResult = (Point)pConverter.ConvertFromString(string1);
// pointResult is equal to (10, 20)
// Displaying Results
syntaxString = "pointResult = (Point)pConverter1.ConvertFromString(string1);";
resultType = "Point";
operationString = "Converting a String to a Point";
ShowResults(pointResult.ToString(), syntaxString, resultType, operationString);
break;
}
case "rb2":
{
// Converts a String to a Vector using a VectorConverter
// Returns a Vector.
VectorConverter vConverter = new VectorConverter();
Vector vectorResult = new Vector();
string string1 = "10,20";
vectorResult = (Vector)vConverter.ConvertFromString(string1);
// vectorResult is equal to (10, 20)
// Displaying Results
syntaxString = "vectorResult = (Vector)vConverter.ConvertFromString(string1);";
resultType = "Vector";
operationString = "Converting a String into a Vector";
ShowResults(vectorResult.ToString(), syntaxString, resultType, operationString);
break;
}
case "rb3":
{
// Converts a String to a Matrix using a MatrixConverter
// Returns a Matrix.
MatrixConverter mConverter = new MatrixConverter();
Matrix matrixResult = new Matrix();
string string2 = "10,20,30,40,50,60";
matrixResult = (Matrix)mConverter.ConvertFromString(string2);
// matrixResult is equal to (10, 20, 30, 40, 50, 60)
// Displaying Results
syntaxString = "matrixResult = (Vector)mConverter.ConvertFromString(string2);";
resultType = "Matrix";
operationString = "Converting a String into a Matrix";
ShowResults(matrixResult.ToString(), syntaxString, resultType, operationString);
break;
}
case "rb4":
{
// Converts a String to a Point3D using a Point3DConverter
// Returns a Point3D.
Point3DConverter p3DConverter = new Point3DConverter();
Point3D point3DResult = new Point3D();
string string3 = "10,20,30";
point3DResult = (Point3D)p3DConverter.ConvertFromString(string3);
// point3DResult is equal to (10, 20, 30)
// Displaying Results
syntaxString = "point3DResult = (Point3D)p3DConverter.ConvertFromString(string3);";
resultType = "Point3D";
operationString = "Converting a String into a Point3D";
ShowResults(point3DResult.ToString(), syntaxString, resultType, operationString);
break;
}
case "rb5":
{
// Converts a String to a Vector3D using a Vector3DConverter
// Returns a Vector3D.
Vector3DConverter v3DConverter = new Vector3DConverter();
Vector3D vector3DResult = new Vector3D();
string string3 = "10,20,30";
vector3DResult = (Vector3D)v3DConverter.ConvertFromString(string3);
// vector3DResult is equal to (10, 20, 30)
// Displaying Results
syntaxString = "vector3DResult = (Vector3D)v3DConverter.ConvertFromString(string3);";
resultType = "Vector3D";
operationString = "Converting a String into a Vector3D";
ShowResults(vector3DResult.ToString(), syntaxString, resultType, operationString);
break;
}
case "rb6":
{
// Converts a String to a Size3D using a Size3DConverter
// Returns a Size3D.
Size3DConverter s3DConverter = new Size3DConverter();
Size3D size3DResult = new Size3D();
string string3 = "10,20,30";
size3DResult = (Size3D)s3DConverter.ConvertFromString(string3);
// size3DResult is equal to (10, 20, 30)
// Displaying Results
syntaxString = "size3DResult = (Size3D)v3DConverter.ConvertFromString(string3);";
resultType = "Size3D";
operationString = "Converting a String into a Size3D";
ShowResults(size3DResult.ToString(), syntaxString, resultType, operationString);
break;
}
case "rb7":
{
// Converts a String to a Point4D using a Point4DConverter
// Returns a Point4D.
Point4DConverter p4DConverter = new Point4DConverter();
Point4D point4DResult = new Point4D();
string string4 = "10,20,30,40";
point4DResult = (Point4D)p4DConverter.ConvertFromString(string4);
// point4DResult is equal to (10, 20, 30)
// Displaying Results
syntaxString = "point4DResult = (Point4D)v3DConverter.ConvertFromString(string3);";
resultType = "Point4D";
operationString = "Converting a String into a Point4D";
ShowResults(point4DResult.ToString(), syntaxString, resultType, operationString);
break;
}
default:
break;
} //end switch
}
/// <summary>
/// Transforms the given point.
/// </summary>
/// <param name="point">Point to transform.</param>
/// <returns>Transformed point.</returns>
public Point4D Transform(Point4D point)
{
return(Value.Transform(point));
}
