//----------------------------------------------------------------------------
void AVector::Orthonormalize (AVector& vec0, AVector& vec1, AVector& vec2)
{
// If the input vectors are v0, v1, and v2, then the Gram-Schmidt
// orthonormalization produces vectors u0, u1, and u2 as follows,
//
// u0 = v0/|v0|
// u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
// u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
//
// where |A| indicates length of vector A and A*B indicates dot
// product of vectors A and B.
// Compute u0.
vec0.Normalize();
// Compute u1.
float dot0 = vec0.Dot(vec1);
vec1 -= dot0*vec0;
vec1.Normalize();
// Compute u2.
float dot1 = vec1.Dot(vec2);
dot0 = vec0.Dot(vec2);
vec2 -= dot0*vec0 + dot1*vec1;
vec2.Normalize();
}
//----------------------------------------------------------------------------
void EditRenderView_Scene::_RolateCamera(float horz, float vert)
{
Scene *scene = PX2_PROJ.GetScene();
CameraActor *camActor = scene->GetUseCameraActor();
if (VT_PERSPECTIVE == mViewType)
{
AVector rVector;
AVector dVector;
AVector uVector;
camActor->GetRDUVector(rVector, dVector, uVector);
// horz
HMatrix incrH(AVector::UNIT_Z, -horz*0.5f);
dVector = incrH * dVector;
uVector = incrH * uVector;
rVector = incrH * rVector;
// vert
Matrix3f kIncrV(rVector, -vert*0.5f);
dVector = kIncrV * dVector;
uVector = kIncrV * uVector;
dVector.Normalize();
float dVectorAdj = dVector.Dot(AVector::UNIT_Z);
float dVectorAdj1 = dVector.Dot(-AVector::UNIT_Z);
if (dVectorAdj > 0.9f || dVectorAdj1 > 0.9f)
return;
AVector::Orthonormalize(dVector, uVector, rVector);
camActor->LocalTransform.SetRotate(HMatrix(rVector, dVector,
uVector, AVector::ZERO, true));
}
}
//----------------------------------------------------------------------------
AVector CurveSegment::Normal (float u) const
{
AVector velocity = PU(u);
AVector acceleration = PUU(u);
float VDotV = velocity.Dot(velocity);
float VDotA = velocity.Dot(acceleration);
AVector normal = VDotV*acceleration - VDotA*velocity;
normal.Normalize();
return normal;
}
//----------------------------------------------------------------------------
void CurveSegment::GetFrame (float u, APoint& position, AVector& tangent,
AVector& normal, AVector& binormal) const
{
position = P(u);
AVector velocity = PU(u);
AVector acceleration = PUU(u);
float VDotV = velocity.Dot(velocity);
float VDotA = velocity.Dot(acceleration);
normal = VDotV*acceleration - VDotA*velocity;
normal.Normalize();
tangent = velocity;
tangent.Normalize();
binormal = tangent.Cross(normal);
}
//----------------------------------------------------------------------------
bool Bound::TestIntersection (const Bound& bound, float tmax,
const AVector& velocity0, const AVector& velocity1) const
{
if (bound.GetRadius() == 0.0f || GetRadius() == 0.0f)
{
return false;
}
AVector relVelocity = velocity1 - velocity0; // 相对速度
AVector cenDiff = bound.mCenter - mCenter; // 相对位移
float a = relVelocity.SquaredLength();
float c = cenDiff.SquaredLength();
float rSum = bound.mRadius + mRadius;
float rSumSqr = rSum*rSum;
if (a > 0.0f)
{
float b = cenDiff.Dot(relVelocity);
if (b <= 0.0f)
{
if (-tmax*a <= b)
{
return a*c - b*b <= a*rSumSqr;
}
else
{
return tmax*(tmax*a + 2.0f*b) + c <= rSumSqr;
}
}
}
return c <= rSumSqr;
}
//----------------------------------------------------------------------------
void HMatrix::MakePerspectiveProjection (const APoint& origin,
const AVector& normal, const APoint& eye)
{
// +- -+
// M = | Dot(N,E-P)*I - E*N^T -(Dot(N,E-P)*I - E*N^T)*E |
// | -N^t Dot(N,E) |
// +- -+
//
// where E is the eye point, P is a point on the plane, and N is a
// unit-length plane normal.
float dotND = normal.Dot(eye - origin);
mEntry[ 0] = dotND - eye[0]*normal[0];
mEntry[ 1] = -eye[0]*normal[1];
mEntry[ 2] = -eye[0]*normal[2];
mEntry[ 3] = -(mEntry[0]*eye[0] + mEntry[1]*eye[1] + mEntry[2]*eye[2]);
mEntry[ 4] = -eye[1]*normal[0];
mEntry[ 5] = dotND - eye[1]*normal[1];
mEntry[ 6] = -eye[1]*normal[2];
mEntry[ 7] = -(mEntry[4]*eye[0] + mEntry[5]*eye[1] + mEntry[6]*eye[2]);
mEntry[ 8] = -eye[2]*normal[0];
mEntry[ 9] = -eye[2]*normal[1];
mEntry[10] = dotND- eye[2]*normal[2];
mEntry[11] = -(mEntry[8]*eye[0] + mEntry[9]*eye[1] + mEntry[10]*eye[2]);
mEntry[12] = -normal[0];
mEntry[13] = -normal[1];
mEntry[14] = -normal[2];
mEntry[15] = eye.Dot(normal);
}
//----------------------------------------------------------------------------
void ClodMeshes::UpdateClods ()
{
// Adjust the triangle quantities for the clod meshes. The distance along
// the camera direction controls the triangle quantities. A nonlinear
// drop-off is used.
for (int i = 0; i < 2; ++i)
{
AVector diff =
mClod[i]->WorldBound.GetCenter() - mCamera->GetPosition();
float depth = diff.Dot(mCamera->GetDVector());
int targetRecord;
if (depth <= mCamera->GetDMin())
{
targetRecord = 0;
}
else if (depth >= mCamera->GetDMax())
{
targetRecord = mClod[i]->GetNumRecords() - 1;
}
else
{
float dmin = mCamera->GetDMin();
float dmax = mCamera->GetDMax();
float ratio = Mathf::Pow((depth - dmin)/(dmax - dmin), 0.5f);
targetRecord = (int)((mClod[i]->GetNumRecords() - 1)*ratio);
}
mClod[i]->TargetRecord() = targetRecord;
}
}
//----------------------------------------------------------------------------
bool PlanarShadowEffect::GetProjectionMatrix (int i, HMatrix& projection)
{
// Compute the equation for the shadow plane in world coordinates.
APoint vertex[3];
mPlanes[i]->GetWorldTriangle(0, vertex);
HPlane worldPlane(vertex[0], vertex[1], vertex[2]);
// This is a conservative test to see whether a shadow should be cast.
// This can cause incorrect results if the caster is large and intersects
// the plane, but ordinarily we are not trying to cast shadows in such
// situations.
if (mShadowCaster->WorldBound.WhichSide(worldPlane) < 0)
{
// The shadow caster is on the far side of plane, so it cannot cast
// a shadow.
return false;
}
// Compute the projection matrix for the light source.
Light* projector = mProjectors[i];
AVector normal = worldPlane.GetNormal();
if (projector->GetType() == Light::LT_DIRECTIONAL)
{
float NdD = normal.Dot(projector->DVector);
if (NdD >= 0.0f)
{
// The projection must be onto the "positive side" of the plane.
return false;
}
projection.MakeObliqueProjection(vertex[0], normal,
projector->DVector);
}
else if (projector->GetType() == Light::LT_POINT
|| projector->GetType() == Light::LT_SPOT)
{
float NdE = projector->Position.Dot(normal);
if (NdE <= 0.0f)
{
// The projection must be onto the "positive side" of the plane.
return false;
}
projection.MakePerspectiveProjection(vertex[0], normal,
projector->Position);
}
else
{
assertion(false, "Light type not supported.\n");
return false;
}
return true;
}
//----------------------------------------------------------------------------
void AmbientRegionActor::_UpdateDirLightCamera()
{
AVector dir = AVector::AnglesToDirection(Mathf::DEG_TO_RAD*mHorAngle,
Mathf::DEG_TO_RAD*mVerAngle);
dir.Normalize();
Scene *scene = DynamicCast<Scene>(GetTopestParent());
if (scene)
{
EnvirParam *envirParam = scene->GetEnvirParam();
Light *lightDir = envirParam->GetLight_Dir();
Projector *projector = envirParam->GetLight_Dir_Projector();
lightDir->Ambient = Float4(mAmbientColor[0], mAmbientColor[1],
mAmbientColor[2], mIntensity);
lightDir->Intensity = mIntensity;
lightDir->Diffuse = Float4(mDiffuseColor[0], mDiffuseColor[1],
mDiffuseColor[2], 1.0f);
lightDir->Specular = Float4(mSpecularColor[0], mSpecularColor[1],
mSpecularColor[2], mSpecularPow);
float upDot = dir.Dot(-AVector::UNIT_Z);
if (upDot >= 0.99f)
{
}
else
{
AVector upTemp = AVector::UNIT_Z;
AVector right = dir.UnitCross(upTemp);
AVector up = right.UnitCross(dir);
lightDir->DVector = dir;
lightDir->UVector = up;
lightDir->RVector = right;
APoint camPos = mLightCameraLookPosition - dir*mLightCameraLookDistance;
projector->SetFrame(camPos, lightDir->DVector,
lightDir->UVector, lightDir->RVector);
}
if (!projector->IsPerspective())
{
projector->SetFrustum(0.1f, 100.0f,
-mLightCameraExtent, mLightCameraExtent, -mLightCameraExtent,
mLightCameraExtent);
}
else
{
projector->SetFrustum(mLightCameraExtent, 1.0f, 1.0f, 100.0f);
}
}
}
//----------------------------------------------------------------------------
void Renderable::GetVisibleSet (Culler& culler, bool)
{
AdjustTransparent();
const Camera *camera = culler.GetCamera();
assertion(camera!=0, "camera must not be 0.");
AVector cameraDir = camera->GetDVector();
AVector diff = WorldBound.GetCenter() - camera->GetPosition();
mEyeDistance = cameraDir.Dot(diff);
culler.Insert(this);
}
//----------------------------------------------------------------------------
void AVector::Orthonormalize (AVector& vec0, AVector& vec1, AVector& vec2)
{
// 输入的向量为v0，v1，v2，按照下面的方式进行Gram-Schmidt正交化
//
// u0 = v0/|v0|
// u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
// u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
//
// |A|代表向量A的长度；A*B代表两个向量“点乘”
// 单位化
vec0.Normalize();
// 计算 u1
float dot0 = vec0.Dot(vec1);
vec1 -= dot0*vec0;
vec1.Normalize();
// 计算 u2
float dot1 = vec1.Dot(vec2);
dot0 = vec0.Dot(vec2);
vec2 -= dot0*vec0 + dot1*vec1;
vec2.Normalize();
}
//----------------------------------------------------------------------------
void EU_CanvasStage::_RolateCamera(float horz, float vert)
{
Scene *scene = PX2_PROJ.GetScene();
horz *= 0.4f;
vert *= 0.25f;
if (VT_PERSPECTIVE == mViewType)
{
AVector rVector;
AVector dVector;
AVector uVector;
mStageCameraNode->LocalTransform.GetRDUVector(rVector, dVector, uVector);
// horz
HMatrix incrH(AVector::UNIT_Z, -horz);
dVector = incrH * dVector;
uVector = incrH * uVector;
rVector = incrH * rVector;
// vert
Matrix3f kIncrV(rVector, -vert);
dVector = kIncrV * dVector;
uVector = kIncrV * uVector;
dVector.Normalize();
float dVectorAdj = dVector.Dot(AVector::UNIT_Z);
float dVectorAdj1 = dVector.Dot(-AVector::UNIT_Z);
if (dVectorAdj > 0.9f || dVectorAdj1 > 0.9f)
return;
AVector::Orthonormalize(dVector, uVector, rVector);
mStageCameraNode->LocalTransform.SetRotate(HMatrix(rVector, dVector,
uVector, AVector::ZERO, true));
}
}
//----------------------------------------------------------------------------
int FramesMesh::_GetDirIndex(const AVector &dir)
{
AVector animVec = dir;
animVec.Normalize();
AVector up = AVector::UNIT_Y;
float dotVal = up.Dot(animVec);
float rad = Mathf::ACos(dotVal);
float degree = Mathf::RAD_TO_DEG * rad;
bool isRight = (dir.X() > 0.0f);
if (0 <= degree && degree < 22.5f)
{
return 0;
}
else if (22.5f <= degree && degree < 67.5f)
{
if (isRight)
return 1;
else
return 7;
}
else if (67.5 <= degree && degree < 112.5f)
{
if (isRight)
return 2;
else
return 6;
}
else if (112.5f <= degree && degree < 157.5f)
{
if (isRight)
return 3;
else
return 5;
}
else if (157.5f <= degree && degree <= 180.0f)
{
return 4;
}
return 0;
}
//----------------------------------------------------------------------------
float CurveSegment::Torsion (float u) const
{
AVector velocity = PU(u);
AVector acceleration = PUU(u);
AVector cross = velocity.Cross(acceleration);
float denom = cross.SquaredLength();
if (denom >= Mathf::ZERO_TOLERANCE)
{
AVector jerk = PUUU(u);
float numer = cross.Dot(jerk);
return numer/denom;
}
else
{
// Torsion is indeterminate, just return 0.
return 0.0f;
}
}
//----------------------------------------------------------------------------
void HMatrix::MakeObliqueProjection (const APoint& origin,
const AVector& normal, const AVector& direction)
{
// The projection plane is Dot(N,X-P) = 0 where N is a 3-by-1 unit-length
// normal vector and P is a 3-by-1 point on the plane. The projection
// is oblique to the plane, in the direction of the 3-by-1 vector D.
// Necessarily Dot(N,D) is not zero for this projection to make sense.
// Given a 3-by-1 point U, compute the intersection of the line U+t*D
// with the plane to obtain t = -Dot(N,U-P)/Dot(N,D). Then
//
// projection(U) = P + [I - D*N^T/Dot(N,D)]*(U-P)
//
// A 4-by-4 homogeneous transformation representing the projection is
//
// +- -+
// M = | D*N^T - Dot(N,D)*I -Dot(N,P)D |
// | 0^T -Dot(N,D) |
// +- -+
//
// where M applies to [U^T 1]^T by M*[U^T 1]^T. The matrix is chosen so
// that M[3][3] > 0 whenever Dot(N,D) < 0 (projection is onto the
// "positive side" of the plane).
float dotND = normal.Dot(direction);
float dotNO = origin.Dot(normal);
mEntry[ 0] = direction[0]*normal[0] - dotND;
mEntry[ 1] = direction[0]*normal[1];
mEntry[ 2] = direction[0]*normal[2];
mEntry[ 3] = -dotNO*direction[0];
mEntry[ 4] = direction[1]*normal[0];
mEntry[ 5] = direction[1]*normal[1] - dotND;
mEntry[ 6] = direction[1]*normal[2];
mEntry[ 7] = -dotNO*direction[1];
mEntry[ 8] = direction[2]*normal[0];
mEntry[ 9] = direction[2]*normal[1];
mEntry[10] = direction[2]*normal[2] - dotND;
mEntry[11] = -dotNO*direction[2];
mEntry[12] = 0.0f;
mEntry[13] = 0.0f;
mEntry[14] = 0.0f;
mEntry[15] = -dotND;
}
//----------------------------------------------------------------------------
bool Bound::TestIntersection (const APoint& origin, const AVector& direction,
float tmin, float tmax) const
{
if (GetRadius() == 0.0f)
{
return false;
}
AVector diff;
float a0, a1, discr;
if (tmin == -Mathf::MAX_REAL)
{
assertion(tmax == Mathf::MAX_REAL,
"tmax must be infinity for a line.\n");
// Test for sphere-line intersection.
diff = origin - mCenter;
a0 = diff.Dot(diff) - mRadius*mRadius;
a1 = direction.Dot(diff);
discr = a1*a1 - a0;
return discr >= 0.0f;
}
if (tmax == Mathf::MAX_REAL)
{
assertion(tmin == 0.0f, "tmin must be zero for a ray.\n");
// Test for sphere-ray intersection.
AVector diff = origin - mCenter;
a0 = diff.Dot(diff) - mRadius*mRadius;
if (a0 <= 0.0f)
{
// The ray origin is inside the sphere.
return true;
}
// else: The ray origin is outside the sphere.
a1 = direction.Dot(diff);
if (a1 >= 0.0f)
{
// The ray forms an acute angle with diff, and so the ray is
// directed from the sphere. Thus, the ray origin is outside
// the sphere, and points P+t*D for t >= 0 are even farther
// away from the sphere.
return false;
}
discr = a1*a1 - a0;
return discr >= 0.0f;
}
assertion(tmax > tmin, "tmin < tmax is required for a segment.\n");
// Test for sphere-segment intersection.
float segExtent = 0.5f*(tmin + tmax);
APoint segOrigin = origin + segExtent*direction;
diff = segOrigin - mCenter;
a0 = diff.Dot(diff) - mRadius*mRadius;
a1 = direction.Dot(diff);
discr = a1*a1 - a0;
if (discr < 0.0f)
{
return false;
}
float tmp0 = segExtent*segExtent + a0;
float tmp1 = 2.0f*a1*segExtent;
float qm = tmp0 - tmp1;
float qp = tmp0 + tmp1;
if (qm*qp <= 0.0f)
{
return true;
}
return qm > 0.0f && Mathf::FAbs(a1) < segExtent;
}
//----------------------------------------------------------------------------
void SceneNodeCtrl::OnMotion(bool leftDown, RenderStep *renderStep,
PX2::APoint posNow, PX2::APoint posBefore)
{
PX2_UNUSED(leftDown);
PX2_UNUSED(renderStep);
Renderer *renderer = renderStep->GetRenderer();
Camera *camera = renderStep->GetCamera();
// 光标移动更新
if (DT_NONE == mDragType)
{
GeoObjFactory factory;
DragType dt = GetDragType(renderStep, posNow);
Movable *ctrlMov = 0;
Float4 colorYellowAlpha = Float4(1.0f, 1.0f, 0.0f, 0.3f);
if (DT_X == dt)
{
ctrlMov = GetCurrentCtrlX();
factory.UpdateCtrlColor(renderer, ctrlMov, Float4::YELLOW);
}
else if (DT_Y == dt)
{
ctrlMov = GetCurrentCtrlY();
factory.UpdateCtrlColor(renderer, ctrlMov, Float4::YELLOW);
}
else if (DT_Z == dt)
{
ctrlMov = GetCurrentCtrlZ();
factory.UpdateCtrlColor(renderer, ctrlMov, Float4::YELLOW);
}
else if (DT_XY == dt)
{
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXY(), colorYellowAlpha);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlYZ(), Float4::ZERO);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXZ(), Float4::ZERO);
}
else if (DT_YZ == dt)
{
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlYZ(), colorYellowAlpha);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXY(), Float4::ZERO);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXZ(), Float4::ZERO);
}
else if (DT_XZ == dt)
{
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXZ(), colorYellowAlpha);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXY(), Float4::ZERO);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlYZ(), Float4::ZERO);
}
else if (DT_XYZ == dt)
{
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXYZ(), Float4::YELLOW);
}
else if (DT_NONE == dt)
{
factory.UpdateCtrlColor(renderer, GetCurrentCtrlX(), Float4::RED);
factory.UpdateCtrlColor(renderer, GetCurrentCtrlY(), Float4::GREEN);
factory.UpdateCtrlColor(renderer, GetCurrentCtrlZ(), Float4::BLUE);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXY(), Float4::ZERO);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlYZ(), Float4::ZERO);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXZ(), Float4::ZERO);
factory.UpdateCtrlColor1(renderer, GetCurrentCtrlXYZ(), Float4::WHITE);
}
if (DT_NONE == dt)
{
Event *ent = EditEventSpace::CreateEventX(EditEventSpace::SceneNodeDrag);
ent->SetData<int>(0);
EventWorld::GetSingleton().BroadcastingLocalEvent(ent);
}
else
{
Event *ent = EditEventSpace::CreateEventX(EditEventSpace::SceneNodeDrag);
ent->SetData<int>(1);
EventWorld::GetSingleton().BroadcastingLocalEvent(ent);
}
}
if (DT_NONE == mDragType) return;
else
{
Event *ent = EditEventSpace::CreateEventX(EditEventSpace::SceneNodeDrag);
ent->SetData<int>(1);
EventWorld::GetSingleton().BroadcastingLocalEvent(ent);
}
int numObjs = PX2_SELECTION.GetNumObjects();
if (0 == numObjs)
return;
// get pickPoint with the plane
TriMesh *meshHelp = PX2_GR.GetXYPlane();
if (DT_X == mDragType)
{
if (LT_PERSPECTIVE == mLookType || LT_TOP == mLookType)
meshHelp = PX2_GR.GetXYPlane();
else if (LT_FRONT == mLookType)
meshHelp = PX2_GR.GetXZPlane();
}
else if (DT_Y == mDragType)
{
meshHelp = PX2_GR.GetXYPlane();
}
else if (DT_Z == mDragType)
{
AVector cameraDir = camera->GetDVector();
cameraDir.Normalize();
float dotVal = Mathf::FAbs(cameraDir.Dot(AVector::UNIT_X));
if (dotVal > 0.7f)
{
meshHelp = PX2_GR.GetYZPlane();
}
else
{
meshHelp = PX2_GR.GetXZPlane();
}
}
else if (DT_XY == mDragType)
{
meshHelp = PX2_GR.GetXYPlane();
}
else if (DT_YZ == mDragType)
{
meshHelp = PX2_GR.GetYZPlane();
}
else if (DT_XZ == mDragType)
{
meshHelp = PX2_GR.GetXZPlane();
}
else if (DT_XYZ == mDragType)
{
meshHelp = PX2_GR.GetXYPlane();
}
meshHelp->WorldTransform.SetTranslate(GetPosition());
// get pick ray
APoint rayOrigin_Now;
AVector rayDir_Now;
renderStep->GetPickRay(posNow.X(), posNow.Z(), rayOrigin_Now, rayDir_Now);
APoint rayOrigin_Before;
AVector rayDir_Before;
renderStep->GetPickRay(posBefore.X(), posBefore.Z(), rayOrigin_Before, rayDir_Before);
// pick
Picker pickerNow;
pickerNow.Execute(meshHelp, rayOrigin_Now, rayDir_Now, 0.0f, Mathf::MAX_REAL);
float lengthNow = pickerNow.GetClosestToZero().T;
APoint positionNow(rayOrigin_Now + rayDir_Now*lengthNow);
Picker pickerOrigin;
pickerOrigin.Execute(meshHelp, rayOrigin_Before, rayDir_Before, 0.0f, Mathf::MAX_REAL);
float lengthBefore = pickerOrigin.GetClosestToZero().T;
APoint positionBefore(rayOrigin_Before + rayDir_Before*lengthBefore);
if (pickerNow.Records.empty() || pickerOrigin.Records.empty()) return;
AVector transMoved = positionNow - positionBefore;
AVector transDir = transMoved;
transDir.Normalize();
float transValue = 0.0f;
float transValue1 = 0.0f;
AVector transVec;
AVector rolateVec;
AVector dirX = mDirX;
AVector dirY = mDirY;
AVector dirZ = mDirZ;
if (DT_X == mDragType)
{
transValue = transMoved.Dot(dirX);
transVec = dirX * transValue;
rolateVec.X() = transMoved.Length() *(1.0f - Mathf::FAbs(transDir.Dot(dirX)));
AVector vec = transDir.Cross(dirX);
rolateVec.X() *= Mathf::Sign(vec.Z());
}
else if (DT_Y == mDragType)
{
transValue = transMoved.Dot(dirY);
transVec = dirY * transValue;
rolateVec.Y() = transMoved.Length() *(1.0f - Mathf::FAbs(transDir.Dot(dirY)));
AVector vec = transDir.Cross(dirY);
rolateVec.Y() *= Mathf::Sign(vec.Z());
}
else if (DT_Z == mDragType)
{
transValue = transMoved.Dot(dirZ);
transVec = dirZ * transValue;
rolateVec.Z() = transMoved.Length() *(1.0f - Mathf::FAbs(transDir.Dot(dirZ)));
rolateVec.Z() *= Mathf::Sign(posNow.X() - posBefore.X());
}
else if (DT_XY == mDragType)
{
transValue = transMoved.Dot(dirX);
transValue1 = transMoved.Dot(dirY);
transVec = dirX * transValue + dirY * transValue1;
}
else if (DT_YZ == mDragType)
{
transValue = transMoved.Dot(dirY);
transValue1 = transMoved.Dot(dirZ);
transVec = dirY * transValue + dirZ * transValue1;
}
else if (DT_XZ == mDragType)
{
transValue = transMoved.Dot(dirX);
transValue1 = transMoved.Dot(dirZ);
transVec = dirX * transValue + dirZ * transValue1;
}
else if (DT_XYZ == mDragType)
{
float transValue0 = Mathf::FAbs(transMoved.Dot(dirX));
float transValue1 = Mathf::FAbs(transMoved.Dot(dirY));
float transValue2 = Mathf::FAbs(transMoved.Dot(dirZ));
float trans = (transValue0 + transValue1 + transValue2) / 3.0f;
trans *= Mathf::Sign(transMoved.Y());
transVec = AVector(trans, trans, trans);
}
if (CT_SCALE == mCtrlType)
transVec *= 0.5f;
HMatrix parentMat = mParentRotateMat.Inverse();
transVec = parentMat * transVec;
if (CT_TRANSLATE == mCtrlType)
{
PX2_SELECTION.Translate(transVec);
UpdateCtrlTrans();
}
else if (CT_ROLATE == mCtrlType)
{
PX2_SELECTION.AddRolate(rolateVec);
}
else if (CT_SCALE == mCtrlType)
{
if (DT_XYZ == mDragType)
PX2_SELECTION.AddScale(transVec);
}
Object *obj = PX2_SELECTION.GetFirstObject();
if (obj)
{
Event *ent = EditEventSpace::CreateEventX(
EditEventSpace::ObjectTransformChanged);
ent->SetData<Object*>(obj);
EventWorld::GetSingleton().BroadcastingLocalEvent(ent);
}
mCtrlsGroup->Update(Time::GetTimeInSeconds(), false);
}
//----------------------------------------------------------------------------
void SurfacePatch::ComputePrincipalCurvatureInfo (float u, float v,
float& curv0, float& curv1, AVector& dir0, AVector& dir1)
{
// Tangents: T0 = dP/du = (x_u,y_u,z_u), T1 = dP/dv = (x_v,y_v,z_v)
// Normal: N = Cross(T0,T1)/Length(Cross(T0,T1))
// Metric Tensor: G = +- -+
// | Dot(T0,T0) Dot(T0,T1) |
// | Dot(T1,T0) Dot(T1,T1) |
// +- -+
//
// Curvature Tensor: B = +- -+
// | -Dot(N,T0_u) -Dot(N,T0_v) |
// | -Dot(N,T1_u) -Dot(N,T1_v) |
// +- -+
//
// Principal curvatures k are the generalized eigenvalues of
//
// Bw = kGw
//
// If k is a curvature and w=(a,b) is the corresponding solution to
// Bw = kGw, then the principal direction as a 3D vector is d = a*U+b*V.
//
// Let k1 and k2 be the principal curvatures. The mean curvature
// is (k1+k2)/2 and the Gaussian curvature is k1*k2.
// Compute the derivatives.
AVector derU = PU(u, v);
AVector derV = PV(u, v);
AVector derUU = PUU(u, v);
AVector derUV = PUV(u, v);
AVector derVV = PVV(u, v);
// Compute the metric tensor.
float metricTensor[2][2];
metricTensor[0][0] = derU.Dot(derU);
metricTensor[0][1] = derU.Dot(derV);
metricTensor[1][0] = metricTensor[0][1];
metricTensor[1][1] = derV.Dot(derV);
// Compute the curvature tensor.
AVector normal = derU.UnitCross(derV);
float curvatureTensor[2][2];
curvatureTensor[0][0] = -normal.Dot(derUU);
curvatureTensor[0][1] = -normal.Dot(derUV);
curvatureTensor[1][0] = curvatureTensor[0][1];
curvatureTensor[1][1] = -normal.Dot(derVV);
// Characteristic polynomial is 0 = det(B-kG) = c2*k^2+c1*k+c0.
float c0 = curvatureTensor[0][0]*curvatureTensor[1][1] -
curvatureTensor[0][1]*curvatureTensor[1][0];
float c1 = 2.0f*curvatureTensor[0][1]* metricTensor[0][1] -
curvatureTensor[0][0]*metricTensor[1][1] -
curvatureTensor[1][1]*metricTensor[0][0];
float c2 = metricTensor[0][0]*metricTensor[1][1] -
metricTensor[0][1]*metricTensor[1][0];
// Principal curvatures are roots of characteristic polynomial.
float temp = Mathf::Sqrt(Mathf::FAbs(c1*c1 - 4.0f*c0*c2));
curv0 = -0.5f*(c1+temp);
curv1 = 0.5f*(-c1+temp);
// Principal directions are solutions to (B-kG)w = 0,
// w1 = (b12-k1*g12,-(b11-k1*g11)) OR (b22-k1*g22,-(b12-k1*g12))
float a0 = curvatureTensor[0][1] - curv0*metricTensor[0][1];
float a1 = curv0*metricTensor[0][0] - curvatureTensor[0][0];
float length = Mathf::Sqrt(a0*a0 + a1*a1);
if (length >= Mathf::ZERO_TOLERANCE)
{
dir0 = a0*derU + a1*derV;
}
else
{
a0 = curvatureTensor[1][1] - curv0*metricTensor[1][1];
a1 = curv0*metricTensor[0][1] - curvatureTensor[0][1];
length = Mathf::Sqrt(a0*a0 + a1*a1);
if (length >= Mathf::ZERO_TOLERANCE)
{
dir0 = a0*derU + a1*derV;
}
else
{
// Umbilic (surface is locally sphere, any direction principal).
dir0 = derU;
}
}
dir0.Normalize();
// Second tangent is cross product of first tangent and normal.
dir1 = dir0.Cross(normal);
}
//----------------------------------------------------------------------------
bool Portal::ReducedFrustum (const Culler& culler,
float reducedFrustum[6])
{
// The portal polygon is transformed into the camera coordinate system
// and projected onto the near plane. An axis-aligned bounding rectangle
// is computed for the projected points and clipped against the left,
// right, bottom, and top frustum planes. The result is itself an
// axis-aligned bounding rectangle that is used to define a "reduced
// frustum" to be used for drawing what is visible through the portal
// polygon.
//
// The algorithm must handle the situation when portal polygon vertices
// are behind the observer. Imagine standing in a room with a doorway
// immediately to your left. Part of the doorway frame is in front of
// you (and visible) and part of it is behind you (and not visible).
// A portal point is represented by P = E + d*D + u*U + r*R, where E is
// the world location for the eye point, D is the camera's world direction
// vector, U is the camera's world up vector, and R is the camera's world
// right vector. The camera coordinates for the portal point are (d,u,r).
// If d > 0, P is in front of the eye point and has a projection onto the
// near plane d = n. If d < 0, P is behind the eye point and does not
// have a projection onto the near plane. If d = 0, P projects to
// "infinity" on the near plane, a problematic case to deal with.
//
// To avoid dealing with d = 0, choose a small value e such that
// 0 < e < n. The portal polygon is clipped against the plane d = e,
// keeping only that portion whose points satisfy d >= e. The clipped
// polygon always has a projection onto the near plane. The axis-aligned
// bounding box for this projection is computed; clipped against the
// left, right, bottom, and top of the frustum; and the result used to
// define the reduced frustum. All this is designed for an inexact
// culling of the objects in the adjacent room, so it is useful to avoid
// preserving the topology of the portal polygon as it is clipped.
// Instead, the portal polygon vertices with d > e are projected and
// the intersection points of portal polygon edges with d = e are
// computed and projected. The axis-aligned bounding box is computed for
// the projections, a process that does not require knowing the polygon
// topology. The algorithm is essentially the one used for clipping a
// convex polygon against the view frustum in the software renderer. The
// polygon vertices are traversed in-order and the signs of the d values
// are updated accordingly. This avoids computing d-signs twice per
// vertex.
const Camera* camera = culler.GetCamera();
const float* frustum = culler.GetFrustum();
float rmin = +Mathf::MAX_REAL; // left
float rmax = -Mathf::MAX_REAL; // right
float umin = +Mathf::MAX_REAL; // bottom
float umax = -Mathf::MAX_REAL; // top
AVector diff;
APoint vertexCam;
int i;
if (camera->IsPerspective())
{
const float epsilon = 1e-6f, invEpsilon = 1e+6f;
int firstSign = 0, lastSign = 0; // in {-1,0,1}
bool signChange = false;
APoint firstVertex = APoint::ORIGIN;
APoint lastVertex = APoint::ORIGIN;
float NdD, UdD, RdD, t;
for (i = 0; i < mNumVertices; i++)
{
diff = mWorldVertices[i] - camera->GetPosition();
vertexCam[0] = diff.Dot(camera->GetDVector());
vertexCam[1] = diff.Dot(camera->GetUVector());
vertexCam[2] = diff.Dot(camera->GetRVector());
vertexCam[3] = 1.0f;
if (vertexCam[0] > epsilon)
{
if (firstSign == 0)
{
firstSign = 1;
firstVertex = vertexCam;
}
NdD = frustum[Camera::VF_DMIN]/vertexCam[0];
UdD = vertexCam[1]*NdD;
RdD = vertexCam[2]*NdD;
if (UdD < umin)
{
umin = UdD;
}
if (UdD > umax)
{
umax = UdD;
}
if (RdD < rmin)
{
rmin = RdD;
}
if (RdD > rmax)
{
rmax = RdD;
}
if (lastSign < 0)
{
signChange = true;
}
lastSign = 1;
}
else
{
if (firstSign == 0)
{
firstSign = -1;
firstVertex = vertexCam;
}
if (lastSign > 0)
{
signChange = true;
}
lastSign = -1;
}
if (signChange)
{
diff = vertexCam - lastVertex;
t = (epsilon - lastVertex[0])/diff[0];
NdD = frustum[Camera::VF_DMIN]*invEpsilon;
UdD = (lastVertex[1] + t*diff[1])*NdD;
RdD = (lastVertex[2] + t*diff[2])*NdD;
if (UdD < umin)
{
umin = UdD;
}
if (UdD > umax)
{
umax = UdD;
}
if (RdD < rmin)
{
rmin = RdD;
}
if (RdD > rmax)
{
rmax = RdD;
}
signChange = false;
}
lastVertex = vertexCam;
}
if (firstSign*lastSign < 0)
{
// Process the last polygon edge.
diff = firstVertex - lastVertex;
t = (epsilon - lastVertex[0])/diff[0];
UdD = (lastVertex[1] + t*diff[1])*invEpsilon;
RdD = (lastVertex[2] + t*diff[2])*invEpsilon;
if (UdD < umin)
{
umin = UdD;
}
if (UdD > umax)
{
umax = UdD;
}
if (RdD < rmin)
{
rmin = RdD;
}
if (RdD > rmax)
{
rmax = RdD;
}
}
}
else
{
for (i = 0; i < mNumVertices; i++)
{
diff = mWorldVertices[i] - camera->GetPosition();
vertexCam[1] = diff.Dot(camera->GetUVector());
vertexCam[2] = diff.Dot(camera->GetRVector());
if (vertexCam[1] < umin)
{
umin = vertexCam[1];
}
if (vertexCam[1] > umax)
{
umax = vertexCam[1];
}
if (vertexCam[2] < rmin)
{
rmin = vertexCam[2];
}
if (vertexCam[2] > rmax)
{
rmax = vertexCam[2];
}
}
}
// Test whether the axis-aligned bounding rectangle is outside the current
// frustum. If it is, the adjoining room need not be visited.
if (frustum[Camera::VF_RMIN] >= rmax ||
frustum[Camera::VF_RMAX] <= rmin ||
frustum[Camera::VF_UMIN] >= umax ||
frustum[Camera::VF_UMAX] <= umin)
{
return false;
}
// The axis-aligned bounding rectangle intersects the current frustum.
// Reduce the frustum for use in drawing the adjoining room.
for (int j = 0; j < 6; ++j)
{
reducedFrustum[j] = frustum[j];
}
if (reducedFrustum[Camera::VF_RMIN] < rmin)
{
reducedFrustum[Camera::VF_RMIN] = rmin;
}
if (reducedFrustum[Camera::VF_RMAX] > rmax)
{
reducedFrustum[Camera::VF_RMAX] = rmax;
}
if (reducedFrustum[Camera::VF_UMIN] < umin)
{
reducedFrustum[Camera::VF_UMIN] = umin;
}
if (reducedFrustum[Camera::VF_UMAX] > umax)
{
reducedFrustum[Camera::VF_UMAX] = umax;
}
return true;
}
//----------------------------------------------------------------------------
void SimpleBumpMapEffect::ComputeLightVectors (Triangles* mesh,
const AVector& worldLightDirection)
{
// The tangent-space coordinates for the light direction vector at each
// vertex is stored in the color0 channel. The computations use the
// vertex normals and the texture coordinates for the base mesh, which
// are stored in the tcoord0 channel. Thus, the mesh must have positions,
// normals, colors (unit 0), and texture coordinates (unit 0).
// The light direction D is in world-space coordinates. Negate it,
// transform it to model-space coordinates, and then normalize it. The
// world-space direction is unit-length, but the geometric primitive
// might have non-unit scaling in its model-to-world transformation, in
// which case the normalization is necessary.
AVector modelLightDirection =
-mesh->WorldTransform.Inverse()*worldLightDirection;
// Set the light vectors to (0,0,0) as a flag that the quantity has not
// yet been computed. The probability that a light vector is actually
// (0,0,0) should be small, so the flag system should save computation
// time overall.
VertexBufferAccessor vba(mesh);
Float3 black(0.0f, 0.0f, 0.0f);
int i;
for (i = 0; i < vba.GetNumVertices(); ++i)
{
vba.Color<Float3>(0, i) = black;
}
int numTriangles = mesh->GetNumTriangles();
for (int t = 0; t < numTriangles; ++t)
{
// Get the triangle vertices and attributes.
int v0, v1, v2;
if (!mesh->GetTriangle(t, v0, v1, v2))
{
continue;
}
APoint position[3] =
{
vba.Position<Float3>(v0),
vba.Position<Float3>(v1),
vba.Position<Float3>(v2)
};
AVector normal[3] =
{
vba.Normal<Float3>(v0),
vba.Normal<Float3>(v1),
vba.Normal<Float3>(v2)
};
Float3* color[3] =
{
&vba.Color<Float3>(0, v0),
&vba.Color<Float3>(0, v1),
&vba.Color<Float3>(0, v2)
};
Float2 tcoord[3] =
{
vba.TCoord<Float2>(0, v0),
vba.TCoord<Float2>(0, v1),
vba.TCoord<Float2>(0, v2)
};
for (i = 0; i < 3; ++i)
{
Float3& colorref = *color[i];
if (colorref != black)
{
continue;
}
int iP = (i == 0) ? 2 : i - 1;
int iN = (i + 1) % 3;
AVector tangent;
if (!ComputeTangent(position[i], tcoord[i], position[iN],
tcoord[iN], position[iP], tcoord[iP], tangent))
{
// The texture coordinate mapping is not properly defined for
// this. Just say that the tangent space light vector points
// in the same direction as the surface normal.
colorref[0] = normal[i][0];
colorref[1] = normal[i][1];
colorref[2] = normal[i][2];
continue;
}
// Project T into the tangent plane by projecting out the surface
// normal N, and then make it unit length.
tangent -= normal[i].Dot(tangent)*(normal[i]);
tangent.Normalize();
// Compute the bitangent B, another tangent perpendicular to T.
AVector bitangent = normal[i].UnitCross(tangent);
// The set {T,B,N} is a right-handed orthonormal set. The
// negated light direction U = -D is represented in this
// coordinate system as
// U = Dot(U,T)*T + Dot(U,B)*B + Dot(U,N)*N
float dotUT = modelLightDirection.Dot(tangent);
float dotUB = modelLightDirection.Dot(bitangent);
float dotUN = modelLightDirection.Dot(normal[i]);
// Transform the light vector into [0,1]^3 to make it a valid
// Float3 object.
colorref[0] = 0.5f*(dotUT + 1.0f);
colorref[1] = 0.5f*(dotUB + 1.0f);
colorref[2] = 0.5f*(dotUN + 1.0f);
}
}
}
//----------------------------------------------------------------------------
void Triangles::UpdateModelTangentsUseTCoords (VertexBufferAccessor& vba)
{
// Each vertex can be visited multiple times, so compute the tangent
// space only on the first visit. Use the zero vector as a flag for the
// tangent vector not being computed.
const int numVertices = vba.GetNumVertices();
bool hasTangent = vba.HasTangent();
Float3 zero(0.0f, 0.0f, 0.0f);
int i;
if (hasTangent)
{
for (i = 0; i < numVertices; ++i)
{
vba.Tangent<Float3>(i) = zero;
}
}
else
{
for (i = 0; i < numVertices; ++i)
{
vba.Binormal<Float3>(i) = zero;
}
}
const int numTriangles = GetNumTriangles();
for (i = 0; i < numTriangles; i++)
{
// Get the triangle vertices' positions, normals, tangents, and
// texture coordinates.
int v0, v1, v2;
if (!GetTriangle(i, v0, v1, v2))
{
continue;
}
APoint locPosition[3] =
{
vba.Position<Float3>(v0),
vba.Position<Float3>(v1),
vba.Position<Float3>(v2)
};
AVector locNormal[3] =
{
vba.Normal<Float3>(v0),
vba.Normal<Float3>(v1),
vba.Normal<Float3>(v2)
};
AVector locTangent[3] =
{
(hasTangent ? vba.Tangent<Float3>(v0) : vba.Binormal<Float3>(v0)),
(hasTangent ? vba.Tangent<Float3>(v1) : vba.Binormal<Float3>(v1)),
(hasTangent ? vba.Tangent<Float3>(v2) : vba.Binormal<Float3>(v2))
};
Float2 locTCoord[3] =
{
vba.TCoord<Float2>(0, v0),
vba.TCoord<Float2>(0, v1),
vba.TCoord<Float2>(0, v2)
};
for (int curr = 0; curr < 3; ++curr)
{
Float3 currLocTangent = (Float3)locTangent[curr];
if (currLocTangent != zero)
{
// This vertex has already been visited.
continue;
}
// Compute the tangent space at the vertex.
AVector norvec = locNormal[curr];
int prev = ((curr + 2) % 3);
int next = ((curr + 1) % 3);
AVector tanvec = ComputeTangent(
locPosition[curr], locTCoord[curr],
locPosition[next], locTCoord[next],
locPosition[prev], locTCoord[prev]);
// Project T into the tangent plane by projecting out the surface
// normal N, and then making it unit length.
tanvec -= norvec.Dot(tanvec)*norvec;
tanvec.Normalize();
// Compute the bitangent B, another tangent perpendicular to T.
AVector binvec = norvec.UnitCross(tanvec);
if (vba.HasTangent())
{
locTangent[curr] = tanvec;
if (vba.HasBinormal())
{
vba.Binormal<Float3>(curr) = binvec;
}
}
else
{
vba.Binormal<Float3>(curr) = tanvec;
}
}
}
}
//----------------------------------------------------------------------------
void Triangles::UpdateModelTangentsUseGeometry (VertexBufferAccessor& vba)
{
// Compute the matrix of normal derivatives.
const int numVertices = vba.GetNumVertices();
HMatrix* dNormal = new1<HMatrix>(numVertices);
HMatrix* wwTrn = new1<HMatrix>(numVertices);
HMatrix* dwTrn = new1<HMatrix>(numVertices);
memset(wwTrn, 0, numVertices*sizeof(HMatrix));
memset(dwTrn, 0, numVertices*sizeof(HMatrix));
const int numTriangles = GetNumTriangles();
int i, row, col;
for (i = 0; i < numTriangles; ++i)
{
// Get the vertex indices for the triangle.
int v[3];
if (!GetTriangle(i, v[0], v[1], v[2]))
{
continue;
}
for (int j = 0; j < 3; j++)
{
// Get the vertex positions and normals.
int v0 = v[j];
int v1 = v[(j + 1) % 3];
int v2 = v[(j + 2) % 3];
APoint pos0 = vba.Position<Float3>(v0);
APoint pos1 = vba.Position<Float3>(v1);
APoint pos2 = vba.Position<Float3>(v2);
AVector nor0 = vba.Normal<Float3>(v0);
AVector nor1 = vba.Normal<Float3>(v1);
AVector nor2 = vba.Normal<Float3>(v2);
// Compute the edge from pos0 to pos1, project it to the tangent
// plane of the vertex, and compute the difference of adjacent
// normals.
AVector edge = pos1 - pos0;
AVector proj = edge - edge.Dot(nor0)*nor0;
AVector diff = nor1 - nor0;
for (row = 0; row < 3; ++row)
{
for (col = 0; col < 3; ++col)
{
wwTrn[v0][row][col] += proj[row]*proj[col];
dwTrn[v0][row][col] += diff[row]*proj[col];
}
}
// Compute the edge from pos0 to pos2, project it to the tangent
// plane of the vertex, and compute the difference of adjacent
// normals.
edge = pos2 - pos0;
proj = edge - edge.Dot(nor0)*nor0;
diff = nor2 - nor0;
for (row = 0; row < 3; ++row)
{
for (col = 0; col < 3; ++col)
{
wwTrn[v0][row][col] += proj[row]*proj[col];
dwTrn[v0][row][col] += diff[row]*proj[col];
}
}
}
}
// Add N*N^T to W*W^T for numerical stability. In theory 0*0^T is added
// to D*W^T, but of course no update is needed in the implementation.
// Compute the matrix of normal derivatives.
for (i = 0; i < numVertices; ++i)
{
AVector nor = vba.Normal<Float3>(i);
for (row = 0; row < 3; ++row)
{
for (col = 0; col < 3; ++col)
{
wwTrn[i][row][col] =
0.5f*wwTrn[i][row][col] + nor[row]*nor[col];
dwTrn[i][row][col] *= 0.5f;
}
}
wwTrn[i].SetColumn(3, APoint::ORIGIN);
dNormal[i] = dwTrn[i]*wwTrn[i].Inverse();
}
delete1(wwTrn);
delete1(dwTrn);
// If N is a unit-length normal at a vertex, let U and V be unit-length
// tangents so that {U, V, N} is an orthonormal set. Define the matrix
// J = [U | V], a 3-by-2 matrix whose columns are U and V. Define J^T
// to be the transpose of J, a 2-by-3 matrix. Let dN/dX denote the
// matrix of first-order derivatives of the normal vector field. The
// shape matrix is
// S = (J^T * J)^{-1} * J^T * dN/dX * J = J^T * dN/dX * J
// where the superscript of -1 denotes the inverse. (The formula allows
// for J built from non-perpendicular vectors.) The matrix S is 2-by-2.
// The principal curvatures are the eigenvalues of S. If k is a principal
// curvature and W is the 2-by-1 eigenvector corresponding to it, then
// S*W = k*W (by definition). The corresponding 3-by-1 tangent vector at
// the vertex is called the principal direction for k, and is J*W. The
// principal direction for the minimum principal curvature is stored as
// the mesh tangent. The principal direction for the maximum principal
// curvature is stored as the mesh bitangent.
for (i = 0; i < numVertices; ++i)
{
// Compute U and V given N.
AVector norvec = vba.Normal<Float3>(i);
AVector uvec, vvec;
AVector::GenerateComplementBasis(uvec, vvec, norvec);
// Compute S = J^T * dN/dX * J. In theory S is symmetric, but
// because we have estimated dN/dX, we must slightly adjust our
// calculations to make sure S is symmetric.
float s01 = uvec.Dot(dNormal[i]*vvec);
float s10 = vvec.Dot(dNormal[i]*uvec);
float sAvr = 0.5f*(s01 + s10);
float smat[2][2] =
{
{ uvec.Dot(dNormal[i]*uvec), sAvr },
{ sAvr, vvec.Dot(dNormal[i]*vvec) }
};
// Compute the eigenvalues of S (min and max curvatures).
float trace = smat[0][0] + smat[1][1];
float det = smat[0][0]*smat[1][1] - smat[0][1]*smat[1][0];
float discr = trace*trace - 4.0f*det;
float rootDiscr = Mathf::Sqrt(Mathf::FAbs(discr));
float minCurvature = 0.5f*(trace - rootDiscr);
// float maxCurvature = 0.5f*(trace + rootDiscr);
// Compute the eigenvectors of S.
AVector evec0(smat[0][1], minCurvature - smat[0][0], 0.0f);
AVector evec1(minCurvature - smat[1][1], smat[1][0], 0.0f);
AVector tanvec, binvec;
if (evec0.SquaredLength() >= evec1.SquaredLength())
{
evec0.Normalize();
tanvec = evec0.X()*uvec + evec0.Y()*vvec;
binvec = norvec.Cross(tanvec);
}
else
{
evec1.Normalize();
tanvec = evec1.X()*uvec + evec1.Y()*vvec;
binvec = norvec.Cross(tanvec);
}
if (vba.HasTangent())
{
vba.Tangent<Float3>(i) = tanvec;
}
if (vba.HasBinormal())
{
vba.Binormal<Float3>(i) = binvec;
}
}
delete1(dNormal);
}
//----------------------------------------------------------------------------
int Culler::WhichSide (const HPlane& plane) const
{
// The plane is N*(X-C) = 0 where the * indicates dot product. The signed
// distance from the camera location E to the plane is N*(E-C).
float NdEmC = plane.DistanceTo(mCamera->GetPosition());
AVector normal = plane.GetNormal();
float NdD = normal.Dot(mCamera->GetDVector());
float NdU = normal.Dot(mCamera->GetUVector());
float NdR = normal.Dot(mCamera->GetRVector());
float FdN = mFrustum[Camera::VF_DMAX]/mFrustum[Camera::VF_DMIN];
int positive = 0, negative = 0;
float sgnDist;
// Check near-plane vertices.
float PDMin = mFrustum[Camera::VF_DMIN]*NdD;
float NUMin = mFrustum[Camera::VF_UMIN]*NdU;
float NUMax = mFrustum[Camera::VF_UMAX]*NdU;
float NRMin = mFrustum[Camera::VF_RMIN]*NdR;
float NRMax = mFrustum[Camera::VF_RMAX]*NdR;
// V = E + dmin*D + umin*U + rmin*R
// N*(V-C) = N*(E-C) + dmin*(N*D) + umin*(N*U) + rmin*(N*R)
sgnDist = NdEmC + PDMin + NUMin + NRMin;
if (sgnDist > 0.0f)
{
positive++;
}
else if (sgnDist < 0.0f)
{
negative++;
}
// V = E + dmin*D + umin*U + rmax*R
// N*(V-C) = N*(E-C) + dmin*(N*D) + umin*(N*U) + rmax*(N*R)
sgnDist = NdEmC + PDMin + NUMin + NRMax;
if (sgnDist > 0.0f)
{
positive++;
}
else if (sgnDist < 0.0f)
{
negative++;
}
// V = E + dmin*D + umax*U + rmin*R
// N*(V-C) = N*(E-C) + dmin*(N*D) + umax*(N*U) + rmin*(N*R)
sgnDist = NdEmC + PDMin + NUMax + NRMin;
if (sgnDist > 0.0f)
{
positive++;
}
else if (sgnDist < 0.0f)
{
negative++;
}
// V = E + dmin*D + umax*U + rmax*R
// N*(V-C) = N*(E-C) + dmin*(N*D) + umax*(N*U) + rmax*(N*R)
sgnDist = NdEmC + PDMin + NUMax + NRMax;
if (sgnDist > 0.0f)
{
positive++;
}
else if (sgnDist < 0.0f)
{
negative++;
}
// check far-plane vertices (s = dmax/dmin)
float PDMax = mFrustum[Camera::VF_DMAX]*NdD;
float FUMin = FdN*NUMin;
float FUMax = FdN*NUMax;
float FRMin = FdN*NRMin;
float FRMax = FdN*NRMax;
// V = E + dmax*D + umin*U + rmin*R
// N*(V-C) = N*(E-C) + dmax*(N*D) + s*umin*(N*U) + s*rmin*(N*R)
sgnDist = NdEmC + PDMax + FUMin + FRMin;
if (sgnDist > 0.0f)
{
positive++;
}
else if (sgnDist < 0.0f)
{
negative++;
}
// V = E + dmax*D + umin*U + rmax*R
// N*(V-C) = N*(E-C) + dmax*(N*D) + s*umin*(N*U) + s*rmax*(N*R)
sgnDist = NdEmC + PDMax + FUMin + FRMax;
if (sgnDist > 0.0f)
{
positive++;
}
else if (sgnDist < 0.0f)
{
negative++;
}
// V = E + dmax*D + umax*U + rmin*R
// N*(V-C) = N*(E-C) + dmax*(N*D) + s*umax*(N*U) + s*rmin*(N*R)
sgnDist = NdEmC + PDMax + FUMax + FRMin;
if (sgnDist > 0.0f)
{
positive++;
}
else if (sgnDist < 0.0f)
{
negative++;
}
// V = E + dmax*D + umax*U + rmax*R
// N*(V-C) = N*(E-C) + dmax*(N*D) + s*umax*(N*U) + s*rmax*(N*R)
sgnDist = NdEmC + PDMax + FUMax + FRMax;
if (sgnDist > 0.0f)
{
positive++;
}
else if (sgnDist < 0.0f)
{
negative++;
}
if (positive > 0)
{
if (negative > 0)
{
// Frustum straddles the plane.
return 0;
}
// Frustum is fully on the positive side.
return +1;
}
// Frustum is fully on the negative side.
return -1;
}