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;
}
internal override RayHitTestParameters RayFromViewportPoint(Point p, Size viewSize, Rect3D boundingRect, out double distanceAdjustment)
{
// The camera may be animating. Take a snapshot of the current value
// and get the property values we need. (Window OS #992662)
Point3D position = Position;
Vector3D lookDirection = LookDirection;
Vector3D upDirection = UpDirection;
Transform3D transform = Transform;
double zn = NearPlaneDistance;
double zf = FarPlaneDistance;
double fov = M3DUtil.DegreesToRadians(FieldOfView);
//
// 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);
// Note: h and w are 1/2 of the inverse of the width/height ratios:
//
// h = 1/(heightDepthRatio) * (1/2)
// w = 1/(widthDepthRatio) * (1/2)
//
// Computation for h is a bit different than what you will find in
// D3DXMatrixPerspectiveFovRH because we have a horizontal rather
// than vertical FoV.
double aspectRatio = M3DUtil.GetAspectRatio(viewSize);
double halfWidthDepthRatio = Math.Tan(fov / 2);
double h = aspectRatio / halfWidthDepthRatio;
double w = 1 / halfWidthDepthRatio;
// To get from projective space to camera space we apply the
// width/height ratios to find our normalized point at 1 unit
// in front of the camera. (1 is convenient, but has no other
// special significance.) See note above about the construction
// of w and h.
Vector3D rayDirection = new Vector3D(np.X / w, np.Y / h, -1);
// Apply the inverse of the view matrix to our rayDirection vector
// to convert it from camera to world space.
//
// NOTE: Because our construction of the ray assumes that the
// viewMatrix translates the position to the origin we pass
// null for the Camera.Transform below and account for it
// later.
Matrix3D viewMatrix = CreateViewMatrix(/* trasform = */ null, ref position, ref lookDirection, ref upDirection);
Matrix3D invView = viewMatrix;
invView.Invert();
invView.MultiplyVector(ref rayDirection);
// The we have the ray direction, now we need the origin. The camera's
// position would work except that we would intersect geometry between
// the camera plane and the near plane so instead we must find the
// point on the project plane where the ray (position, rayDirection)
// intersect (Windows OS #1005064):
//
// | _.> p = camera position
// rd _+" ld = camera look direction
// .-" |ro pp = projection plane
// _.-" | rd = ray direction
// p +"--------+---> ro = desired ray origin on pp
// ld |
// pp
//
// Above we constructed the direction such that it's length projects to
// 1 unit on the lookDirection vector.
//
//
// rd _.>
// .-" rd = unnormalized rayDirection
// _.-" ld = normalized lookDirection (length = 1)
// -"--------->
// ld
//
// So to find the desired rayOrigin on the projection plane we simply do:
Point3D rayOrigin = position + zn * rayDirection;
rayDirection.Normalize();
// Account for the Camera.Transform we ignored during ray construction above.
if (transform != null && transform != Transform3D.Identity)
{
Matrix3D m = transform.Value;
m.MultiplyPoint(ref rayOrigin);
m.MultiplyVector(ref rayDirection);
PrependInverseTransform(m, ref viewMatrix);
}
RayHitTestParameters rayParameters = new RayHitTestParameters(rayOrigin, rayDirection);
//
// Compute HitTestProjectionMatrix
//
Matrix3D projectionMatrix = GetProjectionMatrix(aspectRatio, zn, zf);
// The projectionMatrix takes camera-space 3D points into normalized clip
// space.
// The viewportMatrix will take normalized clip space into
// viewport coordinates, with an additional 2D translation
// to put the ray at the rayOrigin.
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 =
viewMatrix *
projectionMatrix *
viewportMatrix;
//
// Perspective camera doesn't allow negative NearPlanes, so there's
// not much point in adjusting the ray origin. Hence, the
// distanceAdjustment remains 0.
//
distanceAdjustment = 0.0;
return(rayParameters);
}
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 override RayHitTestParameters RayFromViewportPoint(Point p, Size viewSize, Rect3D boundingRect, out double distanceAdjustment)
{
// The camera may be animating. Take a snapshot of the current value
// and get the property values we need. (Window OS #992662)
Point3D position = Position;
Vector3D lookDirection = LookDirection;
Vector3D upDirection = UpDirection;
double zn = NearPlaneDistance;
double zf = FarPlaneDistance;
double width = Width;
//
// 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);
double aspectRatio = M3DUtil.GetAspectRatio(viewSize);
double w = width;
double h = w / aspectRatio;
// Direction is always perpendicular to the viewing surface.
Vector3D direction = new Vector3D(0, 0, -1);
// Apply the inverse of the view matrix to our ray.
Matrix3D viewMatrix = CreateViewMatrix(Transform, ref position, ref lookDirection, ref upDirection);
Matrix3D invView = viewMatrix;
invView.Invert();
// We construct our ray such that the origin resides on the near
// plane. If our near plane is too far from our the bounding box
// of our scene then the results will be inaccurate. (e.g.,
// OrthographicCameras permit negative near planes, so the near
// plane could be at -Inf.)
//
// However, it is permissable to move the near plane nearer to
// the scene bounds without changing what the ray intersects.
// If the near plane is sufficiently far from the scene bounds
// we make this adjustment below to increase precision.
Rect3D transformedBoundingBox =
M3DUtil.ComputeTransformedAxisAlignedBoundingBox(
ref boundingRect,
ref viewMatrix);
// DANGER: The NearPlaneDistance property is specified as a
// distance from the camera position along the
// LookDirection with (Near < Far).
//
// However, when we transform our scene bounds so that
// the camera is aligned with the negative Z-axis the
// relationship inverts (Near > Far) as illustrated
// below:
//
// NearPlane Y FarPlane
// | ^ |
// | | |
// | | (rect.Z + rect.SizeZ) |
// | | o____ |
// | | | | |
// | | | | |
// | | ____o |
// | | (rect.Z) |
// | Camera -> |
// +Z <----------+----------------------------> -Z
// | 0 |
//
// It is surprising, but its the "far" side of the
// transformed scene bounds that determines the near
// plane distance.
double zn2 = -AddEpsilon(transformedBoundingBox.Z + transformedBoundingBox.SizeZ);
if (zn2 > zn)
{
//
// Our near plane is far from our children. Construct a new
// near plane that's closer. Note that this will modify our
// distance computations, so we have to be sure to adjust our
// distances appropriately.
//
distanceAdjustment = zn2 - zn;
zn = zn2;
}
else
{
//
// Our near plane is either close to or in front of our
// children, so let's keep it -- no distance adjustment needed.
//
distanceAdjustment = 0.0;
}
// Our origin is the point normalized to the front of our viewing volume.
// To find our origin's x/y we just need to scale the normalize point by our
// width/height. In camera space we are looking down the negative Z axis
// so we just set Z to be -zn which puts us on the projection plane
// (Windows OS #1005064).
Point3D origin = new Point3D(np.X * (w / 2), np.Y * (h / 2), -zn);
invView.MultiplyPoint(ref origin);
invView.MultiplyVector(ref direction);
RayHitTestParameters rayParameters = new RayHitTestParameters(origin, direction);
//
// Compute HitTestProjectionMatrix
//
Matrix3D projectionMatrix = GetProjectionMatrix(aspectRatio, zn, zf);
// The projectionMatrix takes camera-space 3D points into normalized clip
// space.
// 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 =
viewMatrix *
projectionMatrix *
viewportMatrix;
return(rayParameters);
}
internal override RayHitTestParameters RayFromViewportPoint(Point p, Size viewSize, Rect3D boundingRect, out double distanceAdjustment)
{
// The camera may be animating. Take a snapshot of the current value
// and get the property values we need. (Window OS #992662)
Point3D position = Position;
Vector3D lookDirection = LookDirection;
Vector3D upDirection = UpDirection;
Transform3D transform = Transform;
double zn = NearPlaneDistance;
double zf = FarPlaneDistance;
double fov = M3DUtil.DegreesToRadians(FieldOfView);
//
// 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);
// Note: h and w are 1/2 of the inverse of the width/height ratios:
//
// h = 1/(heightDepthRatio) * (1/2)
// w = 1/(widthDepthRatio) * (1/2)
//
// Computation for h is a bit different than what you will find in
// D3DXMatrixPerspectiveFovRH because we have a horizontal rather
// than vertical FoV.
double aspectRatio = M3DUtil.GetAspectRatio(viewSize);
double halfWidthDepthRatio = Math.Tan(fov/2);
double h = aspectRatio/halfWidthDepthRatio;
double w = 1/halfWidthDepthRatio;
// To get from projective space to camera space we apply the
// width/height ratios to find our normalized point at 1 unit
// in front of the camera. (1 is convenient, but has no other
// special significance.) See note above about the construction
// of w and h.
Vector3D rayDirection = new Vector3D(np.X/w, np.Y/h, -1);
// Apply the inverse of the view matrix to our rayDirection vector
// to convert it from camera to world space.
//
// NOTE: Because our construction of the ray assumes that the
// viewMatrix translates the position to the origin we pass
// null for the Camera.Transform below and account for it
// later.
Matrix3D viewMatrix = CreateViewMatrix(/* trasform = */ null, ref position, ref lookDirection, ref upDirection);
Matrix3D invView = viewMatrix;
invView.Invert();
invView.MultiplyVector(ref rayDirection);
// The we have the ray direction, now we need the origin. The camera's
// position would work except that we would intersect geometry between
// the camera plane and the near plane so instead we must find the
// point on the project plane where the ray (position, rayDirection)
// intersect (Windows OS #1005064):
//
// | _.> p = camera position
// rd _+" ld = camera look direction
// .-" |ro pp = projection plane
// _.-" | rd = ray direction
// p +"--------+---> ro = desired ray origin on pp
// ld |
// pp
//
// Above we constructed the direction such that it's length projects to
// 1 unit on the lookDirection vector.
//
//
// rd _.>
// .-" rd = unnormalized rayDirection
// _.-" ld = normalized lookDirection (length = 1)
// -"--------->
// ld
//
// So to find the desired rayOrigin on the projection plane we simply do:
Point3D rayOrigin = position + zn*rayDirection;
rayDirection.Normalize();
// Account for the Camera.Transform we ignored during ray construction above.
if (transform != null && transform != Transform3D.Identity)
{
Matrix3D m = transform.Value;
m.MultiplyPoint(ref rayOrigin);
m.MultiplyVector(ref rayDirection);
PrependInverseTransform(m, ref viewMatrix);
}
RayHitTestParameters rayParameters = new RayHitTestParameters(rayOrigin, rayDirection);
//
// Compute HitTestProjectionMatrix
//
Matrix3D projectionMatrix = GetProjectionMatrix(aspectRatio, zn, zf);
// The projectionMatrix takes camera-space 3D points into normalized clip
// space.
// The viewportMatrix will take normalized clip space into
// viewport coordinates, with an additional 2D translation
// to put the ray at the rayOrigin.
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 =
viewMatrix *
projectionMatrix *
viewportMatrix;
//
// Perspective camera doesn't allow negative NearPlanes, so there's
// not much point in adjusting the ray origin. Hence, the
// distanceAdjustment remains 0.
//
distanceAdjustment = 0.0;
return rayParameters;
}
internal override RayHitTestParameters RayFromViewportPoint(Point p, Size viewSize, Rect3D boundingRect, out double distanceAdjustment)
{
// The camera may be animating. Take a snapshot of the current value
// and get the property values we need. (Window OS #992662)
Point3D position = Position;
Vector3D lookDirection = LookDirection;
Vector3D upDirection = UpDirection;
double zn = NearPlaneDistance;
double zf = FarPlaneDistance;
double width = Width;
//
// 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);
double aspectRatio = M3DUtil.GetAspectRatio(viewSize);
double w = width;
double h = w/aspectRatio;
// Direction is always perpendicular to the viewing surface.
Vector3D direction = new Vector3D(0, 0, -1);
// Apply the inverse of the view matrix to our ray.
Matrix3D viewMatrix = CreateViewMatrix(Transform, ref position, ref lookDirection, ref upDirection);
Matrix3D invView = viewMatrix;
invView.Invert();
// We construct our ray such that the origin resides on the near
// plane. If our near plane is too far from our the bounding box
// of our scene then the results will be inaccurate. (e.g.,
// OrthographicCameras permit negative near planes, so the near
// plane could be at -Inf.)
//
// However, it is permissable to move the near plane nearer to
// the scene bounds without changing what the ray intersects.
// If the near plane is sufficiently far from the scene bounds
// we make this adjustment below to increase precision.
Rect3D transformedBoundingBox =
M3DUtil.ComputeTransformedAxisAlignedBoundingBox(
ref boundingRect,
ref viewMatrix);
// DANGER: The NearPlaneDistance property is specified as a
// distance from the camera position along the
// LookDirection with (Near < Far).
//
// However, when we transform our scene bounds so that
// the camera is aligned with the negative Z-axis the
// relationship inverts (Near > Far) as illustrated
// below:
//
// NearPlane Y FarPlane
// | ^ |
// | | |
// | | (rect.Z + rect.SizeZ) |
// | | o____ |
// | | | | |
// | | | | |
// | | ____o |
// | | (rect.Z) |
// | Camera -> |
// +Z <----------+----------------------------> -Z
// | 0 |
//
// It is surprising, but its the "far" side of the
// transformed scene bounds that determines the near
// plane distance.
double zn2 = - AddEpsilon(transformedBoundingBox.Z+transformedBoundingBox.SizeZ);
if (zn2 > zn)
{
//
// Our near plane is far from our children. Construct a new
// near plane that's closer. Note that this will modify our
// distance computations, so we have to be sure to adjust our
// distances appropriately.
//
distanceAdjustment = zn2 - zn;
zn = zn2;
}
else
{
//
// Our near plane is either close to or in front of our
// children, so let's keep it -- no distance adjustment needed.
//
distanceAdjustment = 0.0;
}
// Our origin is the point normalized to the front of our viewing volume.
// To find our origin's x/y we just need to scale the normalize point by our
// width/height. In camera space we are looking down the negative Z axis
// so we just set Z to be -zn which puts us on the projection plane
// (Windows OS #1005064).
Point3D origin = new Point3D(np.X*(w/2), np.Y*(h/2), -zn);
invView.MultiplyPoint(ref origin);
invView.MultiplyVector(ref direction);
RayHitTestParameters rayParameters = new RayHitTestParameters(origin, direction);
//
// Compute HitTestProjectionMatrix
//
Matrix3D projectionMatrix = GetProjectionMatrix(aspectRatio, zn, zf);
// The projectionMatrix takes camera-space 3D points into normalized clip
// space.
// 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 =
viewMatrix *
projectionMatrix *
viewportMatrix;
return rayParameters;
}