C# Matrix3D.TranslatePrepend方法代码示例

//.........这里部分代码省略.........
            // 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);

            // 

            
            // 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));
//.........这里部分代码省略.........

//.........这里部分代码省略.........
            // 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;
            
        }