GfRay
GfFrustum::ComputeRay(const GfVec3d &worldSpacePos) const
{
GfVec3d camSpaceToPos = ComputeViewMatrix().Transform(worldSpacePos);
// Compute the camera-space starting point (the viewpoint) and
// direction (toward the point camSpaceToPos).
GfVec3d pos;
GfVec3d dir;
if (_projectionType == Perspective) {
pos = GfVec3d(0);
dir = camSpaceToPos.GetNormalized();
}
else {
pos.Set(camSpaceToPos[0], camSpaceToPos[1], 0.0);
dir = -GfVec3d::ZAxis();
}
// Transform these by the inverse of the view matrix.
const GfMatrix4d &viewInverse = ComputeViewInverse();
GfVec3d rayFrom = viewInverse.Transform(pos);
GfVec3d rayDir = viewInverse.TransformDir(dir);
// Build and return the ray
return GfRay(rayFrom, rayDir);
}
static GfRay _ComputeUntransformedRay(GfFrustum::ProjectionType projectionType,
const GfRange2d &window,
const GfVec2d &windowPos)
{
// Compute position on window, from provided normalized
// (-1 to 1) coordinates.
double winX = _Rescale(windowPos[0], -1.0, 1.0,
window.GetMin()[0], window.GetMax()[0]);
double winY = _Rescale(windowPos[1], -1.0, 1.0,
window.GetMin()[1], window.GetMax()[1]);
// Compute the camera-space starting point (the viewpoint) and
// direction (toward the point on the window).
GfVec3d pos;
GfVec3d dir;
if (projectionType == GfFrustum::Perspective) {
pos = GfVec3d(0);
dir = GfVec3d(winX, winY, -1.0).GetNormalized();
}
else {
pos.Set(winX, winY, 0.0);
dir = -GfVec3d::ZAxis();
}
// Build and return the ray
return GfRay(pos, dir);
}
GfRay
GfFrustum::ComputePickRay(const GfVec3d &worldSpacePos) const
{
GfVec3d camSpaceToPos = ComputeViewMatrix().Transform(worldSpacePos);
// Compute the camera-space starting point (the viewpoint) and
// direction (toward the point camSpaceToPos).
GfVec3d pos;
GfVec3d dir;
if (_projectionType == Perspective) {
pos = GfVec3d(0);
dir = camSpaceToPos.GetNormalized();
}
else {
pos.Set(camSpaceToPos[0], camSpaceToPos[1], 0.0);
dir = -GfVec3d::ZAxis();
}
return _ComputePickRayOffsetToNearPlane(pos, dir);
}
GfQuaternion
GfMatrix3d::ExtractRotationQuaternion() const
{
// This was adapted from the (open source) Open Inventor
// SbRotation::SetValue(const SbMatrix &m)
int i;
// First, find largest diagonal in matrix:
if (_mtx[0][0] > _mtx[1][1])
i = (_mtx[0][0] > _mtx[2][2] ? 0 : 2);
else
i = (_mtx[1][1] > _mtx[2][2] ? 1 : 2);
GfVec3d im;
double r;
if (_mtx[0][0] + _mtx[1][1] + _mtx[2][2] > _mtx[i][i]) {
r = 0.5 * sqrt(_mtx[0][0] + _mtx[1][1] +
_mtx[2][2] + 1);
im.Set((_mtx[1][2] - _mtx[2][1]) / (4.0 * r),
(_mtx[2][0] - _mtx[0][2]) / (4.0 * r),
(_mtx[0][1] - _mtx[1][0]) / (4.0 * r));
}
else {
int j = (i + 1) % 3;
int k = (i + 2) % 3;
double q = 0.5 * sqrt(_mtx[i][i] - _mtx[j][j] -
_mtx[k][k] + 1);
im[i] = q;
im[j] = (_mtx[i][j] + _mtx[j][i]) / (4 * q);
im[k] = (_mtx[k][i] + _mtx[i][k]) / (4 * q);
r = (_mtx[j][k] - _mtx[k][j]) / (4 * q);
}
return GfQuaternion(GfClamp(r, -1.0, 1.0), im);
}
bool
GfRay::Intersect(const GfVec3d &origin,
const GfVec3d &axis,
const double radius,
const double height,
double *enterDistance,
double *exitDistance) const
{
GfVec3d unitAxis = axis.GetNormalized();
// Apex of cone
GfVec3d apex = origin + height * unitAxis;
GfVec3d delta = _startPoint - apex;
GfVec3d u =_direction - GfDot(_direction, unitAxis) * unitAxis;
GfVec3d v = delta - GfDot(delta, unitAxis) * unitAxis;
double p = GfDot(_direction, unitAxis);
double q = GfDot(delta, unitAxis);
double cos2 = GfSqr(height) / (GfSqr(height) + GfSqr(radius));
double sin2 = 1 - cos2;
double a = cos2 * GfDot(u, u) - sin2 * GfSqr(p);
double b = 2.0 * (cos2 * GfDot(u, v) - sin2 * p * q);
double c = cos2 * GfDot(v, v) - sin2 * GfSqr(q);
if (!_SolveQuadratic(a, b, c, enterDistance, exitDistance)) {
return false;
}
// Eliminate any solutions on the double cone
bool enterValid = GfDot(unitAxis, GetPoint(*enterDistance) - apex) <= 0.0;
bool exitValid = GfDot(unitAxis, GetPoint(*exitDistance) - apex) <= 0.0;
if ((!enterValid) && (!exitValid)) {
// Solutions lie only on double cone
return false;
}
if (!enterValid) {
*enterDistance = *exitDistance;
}
else if (!exitValid) {
*exitDistance = *enterDistance;
}
return true;
}
bool
GfRay::Intersect(const GfVec3d &origin,
const GfVec3d &axis,
const double radius,
double *enterDistance,
double *exitDistance) const
{
GfVec3d unitAxis = axis.GetNormalized();
GfVec3d delta = _startPoint - origin;
GfVec3d u = _direction - GfDot(_direction, unitAxis) * unitAxis;
GfVec3d v = delta - GfDot(delta, unitAxis) * unitAxis;
// Quadratic equation for implicit infinite cylinder
double a = GfDot(u, u);
double b = 2.0 * GfDot(u, v);
double c = GfDot(v, v) - GfSqr(radius);
return _SolveQuadratic(a, b, c, enterDistance, exitDistance);
}
GfFrustum &
GfFrustum::Transform(const GfMatrix4d &matrix)
{
// We'll need the old parameters as we build up the new ones, so, work
// on a newly instantiated frustum. We'll replace the contents of
// this frustum with it once we are done. Note that _dirty is true
// by default, so, there is no need to initialize it here.
GfFrustum frustum;
// Copy the projection type
frustum._projectionType = _projectionType;
// Transform the position of the frustum
frustum._position = matrix.Transform(_position);
// Transform the rotation as follows:
// 1. build view and direction vectors
// 2. transform them with the given matrix
// 3. normalize the vectors and cross them to build an orthonormal frame
// 4. construct a rotation matrix
// 5. extract the new rotation from the matrix
// Generate view direction and up vector
GfVec3d viewDir = ComputeViewDirection();
GfVec3d upVec = ComputeUpVector();
// Transform by matrix
GfVec3d viewDirPrime = matrix.TransformDir(viewDir);
GfVec3d upVecPrime = matrix.TransformDir(upVec);
// Normalize. Save the vec size since it will be used to scale near/far.
double scale = viewDirPrime.Normalize();
upVecPrime.Normalize();
// Cross them to get the third axis. Voila. We have an orthonormal frame.
GfVec3d viewRightPrime = GfCross(viewDirPrime, upVecPrime);
viewRightPrime.Normalize();
// Construct a rotation matrix using the axes.
//
// [ right 0 ]
// [ up 1 ]
// [ -viewDir 0 ]
// [ 0 0 0 1 ]
GfMatrix4d rotMatrix;
rotMatrix.SetIdentity();
// first row
rotMatrix[0][0] = viewRightPrime[0];
rotMatrix[0][1] = viewRightPrime[1];
rotMatrix[0][2] = viewRightPrime[2];
// second row
rotMatrix[1][0] = upVecPrime[0];
rotMatrix[1][1] = upVecPrime[1];
rotMatrix[1][2] = upVecPrime[2];
// third row
rotMatrix[2][0] = -viewDirPrime[0];
rotMatrix[2][1] = -viewDirPrime[1];
rotMatrix[2][2] = -viewDirPrime[2];
// Extract rotation
frustum._rotation = rotMatrix.ExtractRotation();
// Since we applied the matrix to the direction vector, we can use
// its length to find out the scaling that needs to applied to the
// near and far plane.
frustum._nearFar = _nearFar * scale;
// Use the same length to scale the view distance
frustum._viewDistance = _viewDistance * scale;
// Transform the reference plane as follows:
//
// - construct two 3D points that are on the reference plane
// (left/bottom and right/top corner of the reference window)
// - transform the points with the given matrix
// - move the window back to one unit from the viewpoint and
// extract the 2D coordinates that would form the new reference
// window
//
// A note on how we do the last "move" of the reference window:
// Using similar triangles and the fact that the reference window
// is one unit away from the viewpoint, one can show that it's
// sufficient to divide the x and y components of the transformed
// corners by the length of the transformed direction vector.
//
// A 2D diagram helps:
//
// |
// |
// | |
// * ------+------------+
// vp |y1 |
// |
// \--d1--/ |y2
//
// \-------d2----------/
//
// So, y1/y2 = d1/d2 ==> y1 = y2 * d1/d2
// Since d1 = 1 ==> y1 = y2 / d2
// The same argument applies to the x coordinate.
//
// NOTE: In an orthographic projection, the last step (division by
// the length of the vector) is skipped.
//
// XXX NOTE2: The above derivation relies on the
// fact that GetReferecePlaneDepth() is 1.0.
// If we ever allow this to NOT be 1, we'll need to fix this up.
const GfVec2d &min = _window.GetMin();
const GfVec2d &max = _window.GetMax();
// Construct the corner points in 3D as follows: construct a starting
// point by using the x and y coordinates of the reference plane and
// -1 as the z coordinate. Add the position of the frustum to generate
// the actual points in world-space coordinates.
GfVec3d leftBottom =
_position + _rotation.TransformDir(GfVec3d(min[0], min[1], -1.0));
GfVec3d rightTop =
_position + _rotation.TransformDir(GfVec3d(max[0], max[1], -1.0));
// Now, transform the corner points by the given matrix
leftBottom = matrix.Transform(leftBottom);
rightTop = matrix.Transform(rightTop);
// Subtract the transformed frustum position from the transformed
// corner points. Then, rotate the points using the rotation that would
// transform the view direction vector back to (0, 0, -1). This brings
// the corner points from the woorld coordinate system into the local
// frustum one.
leftBottom -= frustum._position;
rightTop -= frustum._position;
leftBottom = frustum._rotation.GetInverse().TransformDir(leftBottom);
rightTop = frustum._rotation.GetInverse().TransformDir(rightTop);
// Finally, use the similar triangles trick to bring the corner
// points back at one unit away from the point. These scaled x and
// y coordinates can be directly used to construct the new
// transformed reference plane. Skip the scaling step for an
// orthographic projection, though.
if (_projectionType == Perspective) {
leftBottom /= scale;
rightTop /= scale;
}
frustum._window.SetMin(GfVec2d(leftBottom[0], leftBottom[1]));
frustum._window.SetMax(GfVec2d(rightTop[0], rightTop[1]));
// Note that negative scales in the transform have the potential
// to flip the window. Fix it if necessary.
GfVec2d wMin = frustum._window.GetMin();
GfVec2d wMax = frustum._window.GetMax();
// Make sure left < right
if ( wMin[0] > wMax[0] ) {
std::swap( wMin[0], wMax[0] );
}
// Make sure bottom < top
if ( wMin[1] > wMax[1] ) {
std::swap( wMin[1], wMax[1] );
}
frustum._window.SetMin( wMin );
frustum._window.SetMax( wMax );
*this = frustum;
return *this;
}
/* static */
GT_DataArrayHandle
GusdPrimWrapper::convertPrimvarData( const UsdGeomPrimvar& primvar, UsdTimeCode time ) {
SdfValueTypeName typeName = primvar.GetTypeName();
if( typeName == SdfValueTypeNames->Int )
{
int usdVal;
primvar.Get( &usdVal, time );
return new GT_Int32Array( &usdVal, 1, 1 );
}
else if( typeName == SdfValueTypeNames->Int64 )
{
int64_t usdVal;
primvar.Get( &usdVal, time );
return new GT_Int64Array( &usdVal, 1, 1 );
}
else if( typeName == SdfValueTypeNames->Float )
{
float usdVal;
primvar.Get( &usdVal, time );
return new GT_Real32Array( &usdVal, 1, 1 );
}
else if( typeName == SdfValueTypeNames->Double )
{
double usdVal;
primvar.Get( &usdVal, time );
return new GT_Real64Array( &usdVal, 1, 1 );
}
else if( typeName == SdfValueTypeNames->Float3 )
{
GfVec3f usdVal;
primvar.Get( &usdVal, time );
return new GT_Real32Array( usdVal.data(), 1, 3 );
}
else if( typeName == SdfValueTypeNames->Double3 )
{
GfVec3d usdVal;
primvar.Get( &usdVal, time );
return new GT_Real64Array( usdVal.data(), 1, 3 );
}
else if( typeName == SdfValueTypeNames->Color3f )
{
GfVec3f usdVal;
primvar.Get( &usdVal, time );
return new GT_Real32Array( usdVal.data(), 1, 3, GT_TYPE_COLOR );
}
else if( typeName == SdfValueTypeNames->Color3d )
{
GfVec3d usdVal;
primvar.Get( &usdVal, time );
return new GT_Real64Array( usdVal.data(), 1, 3, GT_TYPE_COLOR );
}
else if( typeName == SdfValueTypeNames->Normal3f )
{
GfVec3f usdVal;
primvar.Get( &usdVal, time );
return new GT_Real32Array( usdVal.data(), 1, 3, GT_TYPE_NORMAL );
}
else if( typeName == SdfValueTypeNames->Normal3d )
{
GfVec3d usdVal;
primvar.Get( &usdVal, time );
return new GT_Real64Array( usdVal.data(), 1, 3, GT_TYPE_NORMAL );
}
else if( typeName == SdfValueTypeNames->Point3f )
{
GfVec3f usdVal;
primvar.Get( &usdVal, time );
return new GT_Real32Array( usdVal.data(), 1, 3, GT_TYPE_POINT );
}
else if( typeName == SdfValueTypeNames->Point3d )
{
GfVec3d usdVal;
primvar.Get( &usdVal, time );
return new GT_Real64Array( usdVal.data(), 1, 3, GT_TYPE_POINT );
}
else if( typeName == SdfValueTypeNames->Float4 )
{
GfVec4f usdVal;
primvar.Get( &usdVal, time );
return new GT_Real32Array( usdVal.data(), 1, 4 );
}
else if( typeName == SdfValueTypeNames->Double4 )
{
GfVec4d usdVal;
primvar.Get( &usdVal, time );
return new GT_Real64Array( usdVal.data(), 1, 4 );
}
else if( typeName == SdfValueTypeNames->Quatf )
{
GfVec4f usdVal;
primvar.Get( &usdVal, time );
return new GT_Real32Array( usdVal.data(), 1, 4, GT_TYPE_QUATERNION );
}
else if( typeName == SdfValueTypeNames->Quatd )
{
GfVec4d usdVal;
primvar.Get( &usdVal, time );
return new GT_Real64Array( usdVal.data(), 1, 4, GT_TYPE_QUATERNION );
}
else if( typeName == SdfValueTypeNames->Matrix3d )
{
GfMatrix3d usdVal;
primvar.Get( &usdVal, time );
return new GT_Real64Array( usdVal.GetArray(), 1, 9, GT_TYPE_MATRIX3 );
}
else if( typeName == SdfValueTypeNames->Matrix4d ||
typeName == SdfValueTypeNames->Frame4d )
{
GfMatrix4d usdVal;
primvar.Get( &usdVal, time );
return new GT_Real64Array( usdVal.GetArray(), 1, 16, GT_TYPE_MATRIX );
}
else if( typeName == SdfValueTypeNames->String )
{
string usdVal;
primvar.Get( &usdVal, time );
auto gtString = new GT_DAIndexedString( 1 );
gtString->setString( 0, 0, usdVal.c_str() );
return gtString;
}
else if( typeName == SdfValueTypeNames->StringArray )
{
VtArray<string> usdVal;
primvar.ComputeFlattened( &usdVal, time );
auto gtString = new GT_DAIndexedString( usdVal.size() );
for( size_t i = 0; i < usdVal.size(); ++i )
gtString->setString( i, 0, usdVal[i].c_str() );
return gtString;
}
else if( typeName == SdfValueTypeNames->IntArray )
{
VtArray<int> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<int>(usdVal);
}
else if( typeName == SdfValueTypeNames->Int64Array )
{
VtArray<int64_t> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<int64_t>(usdVal);
}
else if( typeName == SdfValueTypeNames->FloatArray )
{
VtArray<float> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<float>(usdVal);
}
else if( typeName == SdfValueTypeNames->DoubleArray )
{
VtArray<double> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<double>(usdVal);
}
else if( typeName == SdfValueTypeNames->Float2Array )
{
VtArray<GfVec2f> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec2f>(usdVal);
}
else if( typeName == SdfValueTypeNames->Double2Array )
{
VtArray<GfVec2d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec2d>(usdVal);
}
else if( typeName == SdfValueTypeNames->Float3Array )
{
VtArray<GfVec3f> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3f>(usdVal);
}
else if( typeName == SdfValueTypeNames->Double3Array )
{
VtArray<GfVec3d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3d>(usdVal);
}
else if( typeName == SdfValueTypeNames->Color3fArray )
{
VtArray<GfVec3f> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3f>(usdVal,GT_TYPE_COLOR);
}
else if( typeName == SdfValueTypeNames->Color3dArray )
{
VtArray<GfVec3d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3d>(usdVal,GT_TYPE_COLOR);
}
else if( typeName == SdfValueTypeNames->Vector3fArray )
{
VtArray<GfVec3f> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3f>(usdVal, GT_TYPE_VECTOR);
}
else if( typeName == SdfValueTypeNames->Vector3dArray )
{
VtArray<GfVec3d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3d>(usdVal, GT_TYPE_VECTOR);
}
else if( typeName == SdfValueTypeNames->Normal3fArray )
{
VtArray<GfVec3f> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3f>(usdVal, GT_TYPE_NORMAL);
}
else if( typeName == SdfValueTypeNames->Normal3dArray )
{
VtArray<GfVec3d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3d>(usdVal, GT_TYPE_NORMAL);
}
else if( typeName == SdfValueTypeNames->Point3fArray )
{
VtArray<GfVec3f> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3f>(usdVal, GT_TYPE_POINT);
}
else if( typeName == SdfValueTypeNames->Point3dArray )
{
VtArray<GfVec3d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec3d>(usdVal, GT_TYPE_POINT);
}
else if( typeName == SdfValueTypeNames->Float4Array )
{
VtArray<GfVec4f> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec4f>(usdVal);
}
else if( typeName == SdfValueTypeNames->Double4Array )
{
VtArray<GfVec4d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec4d>(usdVal);
}
else if( typeName == SdfValueTypeNames->QuatfArray )
{
VtArray<GfVec4f> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec4f>(usdVal, GT_TYPE_QUATERNION);
}
else if( typeName == SdfValueTypeNames->QuatdArray )
{
VtArray<GfVec4d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfVec4d>(usdVal, GT_TYPE_QUATERNION);
}
else if( typeName == SdfValueTypeNames->Matrix3dArray )
{
VtArray<GfMatrix3d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfMatrix3d>(usdVal, GT_TYPE_MATRIX3);
}
else if( typeName == SdfValueTypeNames->Matrix4dArray ||
typeName == SdfValueTypeNames->Frame4dArray )
{
VtArray<GfMatrix4d> usdVal;
primvar.ComputeFlattened( &usdVal, time );
return new GusdGT_VtArray<GfMatrix4d>(usdVal, GT_TYPE_MATRIX);
}
return NULL;
}
void
GfPlane::Set(const GfVec3d &normal, const GfVec3d &point)
{
_normal = normal.GetNormalized();
_distance = GfDot(_normal, point);
}