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);
}
//------------------------------------------------------
//
// Private Methods
//
//------------------------------------------------------
#region Private Methods
//
// Processes a ray-triangle intersection to see if it's a valid hit. Unnecessary faces
// have already been culled by the ray-triange intersection routines.
//
// Shares some code with ValidateLineHit
//
private void ValidateRayHit(
RayHitTestParameters rayParams,
ref Point3D origin,
ref Vector3D direction,
double hitTime,
int i0,
int i1,
int i2,
ref Point barycentric
)
{
if (hitTime > 0)
{
Matrix3D worldTransformMatrix = rayParams.HasWorldTransformMatrix ? rayParams.WorldTransformMatrix : Matrix3D.Identity;
Point3D pointHit = origin + hitTime * direction;
Point3D worldPointHit = pointHit;
worldTransformMatrix.MultiplyPoint(ref worldPointHit);
// If we have a HitTestProjectionMatrix than this hit test originated
// at a Viewport3DVisual.
if (rayParams.HasHitTestProjectionMatrix)
{
// To test if we are in front of the far clipping plane what we
// do conceptually is project our hit point in world space into
// homogenous space and verify that it is on the correct side of
// the Z=1 plane.
//
// To save some cycles we only bother computing Z and W of the
// projected point and use a simple Z/W > 1 test to see if we
// are past the far plane.
//
// NOTE: HitTestProjectionMatrix is not just the camera matrices.
// It has an additional translation to move the ray to the
// origin. This extra translation does not effect this test.
Matrix3D m = rayParams.HitTestProjectionMatrix;
// We directly substitute 1 for p.W below:
double pz = worldPointHit.X * m.M13 + worldPointHit.Y * m.M23 + worldPointHit.Z * m.M33 + m.OffsetZ;
double pw = worldPointHit.X * m.M14 + worldPointHit.Y * m.M24 + worldPointHit.Z * m.M34 + m.M44;
// Early exit if pz/pw > 1. The negated logic is to reject NaNs.
if (!(pz / pw <= 1))
{
return;
}
Debug.Assert(!double.IsInfinity(pz / pw) && !double.IsNaN(pz / pw),
"Expected near/far tests to cull -Inf/+Inf and NaN.");
}
double dist = (worldPointHit - rayParams.Origin).Length;
Debug.Assert(dist > 0, "Distance is negative: " + dist);
if (rayParams.HasModelTransformMatrix)
{
rayParams.ModelTransformMatrix.MultiplyPoint(ref pointHit);
}
rayParams.ReportResult(this, pointHit, dist, i0, i1, i2, barycentric);
}
}
//
// Processes a ray-line intersection to see if it's a valid hit.
//
// Shares some code with ValidateRayHit
//
private void ValidateLineHit(
RayHitTestParameters rayParams,
FaceType facesToHit,
int i0,
int i1,
int i2,
ref Point3D v0,
ref Point3D v1,
ref Point3D v2,
ref Point barycentric
)
{
Matrix3D worldTransformMatrix = rayParams.HasWorldTransformMatrix ? rayParams.WorldTransformMatrix : Matrix3D.Identity;
// OK, we have an intersection with the LINE but that could be wrong on three
// accounts:
// 1. We could have hit the line on the wrong side of the ray's origin.
// 2. We may need to cull the intersection if it's beyond the far clipping
// plane (only if the hit test originated from a Viewport3DVisual.)
// 3. We could have hit a back-facing triangle
// We will transform the hit point back into world space to check these
// things & compute the correct distance from the origin to the hit point.
// Hit point in model space
Point3D pointHit = M3DUtil.Interpolate(ref v0, ref v1, ref v2, ref barycentric);
Point3D worldPointHit = pointHit;
worldTransformMatrix.MultiplyPoint(ref worldPointHit);
// Vector from origin to hit point
Vector3D hitVector = worldPointHit - rayParams.Origin;
Vector3D originalDirection = rayParams.Direction;
double rayDistanceUnnormalized = Vector3D.DotProduct(originalDirection, hitVector);
if (rayDistanceUnnormalized > 0)
{
// If we have a HitTestProjectionMatrix than this hit test originated
// at a Viewport3DVisual.
if (rayParams.HasHitTestProjectionMatrix)
{
// To test if we are in front of the far clipping plane what we
// do conceptually is project our hit point in world space into
// homogenous space and verify that it is on the correct side of
// the Z=1 plane.
//
// To save some cycles we only bother computing Z and W of the
// projected point and use a simple Z/W > 1 test to see if we
// are past the far plane.
//
// NOTE: HitTestProjectionMatrix is not just the camera matrices.
// It has an additional translation to move the ray to the
// origin. This extra translation does not effect this test.
Matrix3D m = rayParams.HitTestProjectionMatrix;
// We directly substitute 1 for p.W below:
double pz = worldPointHit.X * m.M13 + worldPointHit.Y * m.M23 + worldPointHit.Z * m.M33 + m.OffsetZ;
double pw = worldPointHit.X * m.M14 + worldPointHit.Y * m.M24 + worldPointHit.Z * m.M34 + m.M44;
// Early exit if pz/pw > 1. The negated logic is to reject NaNs.
if (!(pz / pw <= 1))
{
return;
}
Debug.Assert(!double.IsInfinity(pz / pw) && !double.IsNaN(pz / pw),
"Expected near/far tests to cull -Inf/+Inf and NaN.");
}
Point3D a = v0, b = v1, c = v2;
worldTransformMatrix.MultiplyPoint(ref a);
worldTransformMatrix.MultiplyPoint(ref b);
worldTransformMatrix.MultiplyPoint(ref c);
Vector3D normal = Vector3D.CrossProduct(b - a, c - a);
double cullSign = -Vector3D.DotProduct(normal, hitVector);
double det = worldTransformMatrix.Determinant;
bool frontFace = (cullSign > 0) == (det >= 0);
if (((facesToHit & FaceType.Front) == FaceType.Front && frontFace) || ((facesToHit & FaceType.Back) == FaceType.Back && !frontFace))
{
double dist = hitVector.Length;
if (rayParams.HasModelTransformMatrix)
{
rayParams.ModelTransformMatrix.MultiplyPoint(ref pointHit);
}
rayParams.ReportResult(this, pointHit, dist, i0, i1, i2, barycentric);
}
}
}
public static void Transform(Matrix3D modelMatrix,
ref Point3D origin, ref Vector3D direction, out bool isRay)
{
if (modelMatrix.InvertCore())
{
Point4D o = new Point4D(origin.X,origin.Y,origin.Z,1);
Point4D d = new Point4D(direction.X,direction.Y,direction.Z,0);
modelMatrix.MultiplyPoint(ref o);
modelMatrix.MultiplyPoint(ref d);
if (o.W == 1 && d.W == 0)
{
// Affine transformation
origin = new Point3D(o.X, o.Y, o.Z);
direction = new Vector3D(d.X, d.Y, d.Z);
isRay = true;
}
else
{
// Non-affine transformation (likely projection)
// Form 4x2 matrix with two points on line in two columns.
double[,] linepoints = new double[,]{{o.X,d.X},{o.Y,d.Y},{o.Z,d.Z},{o.W,d.W}};
ColumnsToAffinePointVector(linepoints,0,1,out origin, out direction);
isRay = false;
}
}
else
{
TransformSingular(ref modelMatrix, ref origin, ref direction);
isRay = false;
}
}