class Geom_Surface;
DEFINE_STANDARD_HANDLE(Geom_Surface, Geom_Geometry)
-//! Describes the common behavior of surfaces in 3D
-//! space. The Geom package provides many
-//! implementations of concrete derived surfaces, such as
-//! planes, cylinders, cones, spheres and tori, surfaces of
-//! linear extrusion, surfaces of revolution, Bezier and
-//! BSpline surfaces, and so on.
-//! The key characteristic of these surfaces is that they
-//! are parameterized. Geom_Surface demonstrates:
-//! - how to work with the parametric equation of a
-//! surface to compute the point of parameters (u,
-//! v), and, at this point, the 1st, 2nd ... Nth derivative,
+//! Describes the common behavior of surfaces in 3D space.
+//! The Geom package provides many implementations of concrete derived surfaces,
+//! such as planes, cylinders, cones, spheres and tori, surfaces of linear extrusion,
+//! surfaces of revolution, Bezier and BSpline surfaces, and so on.
+//! The key characteristic of these surfaces is that they are parameterized.
+//! Geom_Surface demonstrates:
+//! - how to work with the parametric equation of a surface
+//! to compute the point of parameters (u, v), and, at this point, the 1st, 2nd ... Nth derivative;
//! - how to find global information about a surface in
-//! each parametric direction (for example, level of
-//! continuity, whether the surface is closed, its
-//! periodicity, the bounds of the parameters and so on), and
-//! - how the parameters change when geometric
-//! transformations are applied to the surface, or the
-//! orientation is modified.
-//! Note that all surfaces must have a geometric
-//! continuity, and any surface is at least "C0". Generally,
-//! continuity is checked at construction time or when the
-//! curve is edited. Where this is not the case, the
-//! documentation makes this explicit.
+//! each parametric direction (for example, level of continuity, whether the surface is closed,
+//! its periodicity, the bounds of the parameters and so on);
+//! - how the parameters change when geometric transformations are applied to the surface,
+//! or the orientation is modified.
+//!
+//! Note that all surfaces must have a geometric continuity, and any surface is at least "C0".
+//! Generally, continuity is checked at construction time or when the curve is edited.
+//! Where this is not the case, the documentation makes this explicit.
+//!
//! Warning
//! The Geom package does not prevent the construction of
//! surfaces with null areas, or surfaces which self-intersect.
//! equal to Precision::Infinite: instead of Standard_Real::LastReal.
Standard_EXPORT virtual void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const = 0;
- //! Checks whether this surface is closed in the u
- //! parametric direction.
- //! Returns true if, in the u parametric direction: taking
- //! uFirst and uLast as the parametric bounds in
- //! the u parametric direction, for each parameter v, the
- //! distance between the points P(uFirst, v) and
+ //! Checks whether this surface is closed in the u parametric direction.
+ //! Returns true if, in the u parametric direction:
+ //! taking uFirst and uLast as the parametric bounds in
+ //! the u parametric direction, for each parameter v,
+ //! the distance between the points P(uFirst, v) and
//! P(uLast, v) is less than or equal to gp::Resolution().
Standard_EXPORT virtual Standard_Boolean IsUClosed() const = 0;
- //! Checks whether this surface is closed in the u
- //! parametric direction.
- //! Returns true if, in the v parametric
- //! direction: taking vFirst and vLast as the
- //! parametric bounds in the v parametric direction, for
- //! each parameter u, the distance between the points
- //! P(u, vFirst) and P(u, vLast) is less than
- //! or equal to gp::Resolution().
+ //! Checks whether this surface is closed in the u parametric direction.
+ //! Returns true if, in the v parametric direction:
+ //! taking vFirst and vLast as the parametric bounds in the v parametric direction,
+ //! for each parameter u, the distance between the points
+ //! P(u, vFirst) and P(u, vLast) is less than or equal to gp::Resolution().
Standard_EXPORT virtual Standard_Boolean IsVClosed() const = 0;
- //! Checks if this surface is periodic in the u
- //! parametric direction. Returns true if:
+ //! Checks if this surface is periodic in the u parametric direction.
+ //! Returns true if:
//! - this surface is closed in the u parametric direction, and
//! - there is a constant T such that the distance
- //! between the points P (u, v) and P (u + T,
- //! v) (or the points P (u, v) and P (u, v +
- //! T)) is less than or equal to gp::Resolution().
+ //! between the points P (u, v) and P (u + T, v)
+ //! (or the points P (u, v) and P (u, v + T)) is less than or equal to gp::Resolution().
+ //!
//! Note: T is the parametric period in the u parametric direction.
Standard_EXPORT virtual Standard_Boolean IsUPeriodic() const = 0;
- //! Returns the period of this surface in the u
- //! parametric direction.
- //! raises if the surface is not uperiodic.
+ //! Returns the period of this surface in the u parametric direction.
+ //! Raises if the surface is not uperiodic.
Standard_EXPORT virtual Standard_Real UPeriod() const;
- //! Checks if this surface is periodic in the v
- //! parametric direction. Returns true if:
+ //! Checks if this surface is periodic in the v parametric direction.
+ //! Returns true if:
//! - this surface is closed in the v parametric direction, and
//! - there is a constant T such that the distance
- //! between the points P (u, v) and P (u + T,
- //! v) (or the points P (u, v) and P (u, v +
- //! T)) is less than or equal to gp::Resolution().
+ //! between the points P (u, v) and P (u + T, v)
+ //! (or the points P (u, v) and P (u, v + T)) is less than or equal to gp::Resolution().
+ //!
//! Note: T is the parametric period in the v parametric direction.
Standard_EXPORT virtual Standard_Boolean IsVPeriodic() const = 0;
Standard_EXPORT virtual Handle(Geom_Curve) VIso (const Standard_Real V) const = 0;
//! Returns the Global Continuity of the surface in direction U and V :
- //! C0 : only geometric continuity,
- //! C1 : continuity of the first derivative all along the surface,
- //! C2 : continuity of the second derivative all along the surface,
- //! C3 : continuity of the third derivative all along the surface,
- //! G1 : tangency continuity all along the surface,
- //! G2 : curvature continuity all along the surface,
- //! CN : the order of continuity is infinite.
- //! Example :
+ //! - C0: only geometric continuity,
+ //! - C1: continuity of the first derivative all along the surface,
+ //! - C2: continuity of the second derivative all along the surface,
+ //! - C3: continuity of the third derivative all along the surface,
+ //! - G1: tangency continuity all along the surface,
+ //! - G2: curvature continuity all along the surface,
+ //! - CN: the order of continuity is infinite.
+ //!
+ //! Example:
//! If the surface is C1 in the V parametric direction and C2
//! in the U parametric direction Shape = C1.
Standard_EXPORT virtual GeomAbs_Shape Continuity() const = 0;
- //! Returns the order of continuity of the surface in the
- //! U parametric direction.
+ //! Returns the order of continuity of the surface in the U parametric direction.
//! Raised if N < 0.
Standard_EXPORT virtual Standard_Boolean IsCNu (const Standard_Integer N) const = 0;
- //! Returns the order of continuity of the surface in the
- //! V parametric direction.
+ //! Returns the order of continuity of the surface in the V parametric direction.
//! Raised if N < 0.
Standard_EXPORT virtual Standard_Boolean IsCNv (const Standard_Integer N) const = 0;
Standard_EXPORT virtual void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const = 0;
- //! Computes the point P and the first derivatives in the
- //! directions U and V at this point.
+ //! Computes the point P and the first derivatives in the directions U and V at this point.
//! Raised if the continuity of the surface is not C1.
+ //!
+ //! Tip: use GeomLib::NormEstim() to calculate surface normal at specified (U, V) point.
Standard_EXPORT virtual void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const = 0;
//! Computes the point P, the first and the second derivatives in
//! Raised if the continuity of the surface is not C2.
Standard_EXPORT virtual void D3 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V, gp_Vec& D2U, gp_Vec& D2V, gp_Vec& D2UV, gp_Vec& D3U, gp_Vec& D3V, gp_Vec& D3UUV, gp_Vec& D3UVV) const = 0;
- //! ---Purpose ;
- //! Computes the derivative of order Nu in the direction U and Nv
- //! in the direction V at the point P(U, V).
+ //! Computes the derivative of order Nu in the direction U and Nv in the direction V at the point P(U, V).
//!
- //! Raised if the continuity of the surface is not CNu in the U
- //! direction or not CNv in the V direction.
+ //! Raised if the continuity of the surface is not CNu in the U direction or not CNv in the V direction.
//! Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Standard_EXPORT virtual gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const = 0;
- //! Computes the point of parameter U on the surface.
+ //! Computes the point of parameter (U, V) on the surface.
//!
- //! It is implemented with D0
+ //! It is implemented with D0.
+ //! Tip: use GeomLib::NormEstim() to calculate surface normal at specified (U, V) point.
//!
- //! Raised only for an "OffsetSurface" if it is not possible to
- //! compute the current point.
+ //! Raised only for an "OffsetSurface" if it is not possible to compute the current point.
Standard_EXPORT gp_Pnt Value (const Standard_Real U, const Standard_Real V) const;
//! Dumps the content of me into the stream
//=======================================================================
//function : NormEstim
-//purpose :
+//purpose :
//=======================================================================
-
-Standard_Integer GeomLib::NormEstim(const Handle(Geom_Surface)& S,
- const gp_Pnt2d& UV,
- const Standard_Real Tol, gp_Dir& N)
+Standard_Integer GeomLib::NormEstim (const Handle(Geom_Surface)& theSurf,
+ const gp_Pnt2d& theUV,
+ const Standard_Real theTol,
+ gp_Dir& theNorm)
{
- gp_Vec DU, DV;
- gp_Pnt DummyPnt;
- Standard_Real aTol2 = Square(Tol);
+ const Standard_Real aTol2 = Square (theTol);
- S->D1(UV.X(), UV.Y(), DummyPnt, DU, DV);
+ gp_Vec DU, DV;
+ gp_Pnt aDummyPnt;
+ theSurf->D1 (theUV.X(), theUV.Y(), aDummyPnt, DU, DV);
- Standard_Real MDU = DU.SquareMagnitude(), MDV = DV.SquareMagnitude();
+ const Standard_Real MDU = DU.SquareMagnitude(), MDV = DV.SquareMagnitude();
+ if (MDU >= aTol2
+ && MDV >= aTol2)
+ {
+ gp_Vec aNorm = DU ^ DV;
+ Standard_Real aMagn = aNorm.SquareMagnitude();
+ if (aMagn < aTol2)
+ {
+ return 3;
+ }
- if(MDU >= aTol2 && MDV >= aTol2) {
- gp_Vec Norm = DU^DV;
- Standard_Real Magn = Norm.SquareMagnitude();
- if(Magn < aTol2) return 3;
+ theNorm.SetXYZ (aNorm.XYZ());
+ return 0;
+ }
- //Magn = sqrt(Magn);
- N.SetXYZ(Norm.XYZ());
+ gp_Vec D2U, D2V, D2UV;
+ Standard_Boolean isDone = false;
+ CSLib_NormalStatus aStatus;
+ gp_Dir aNormal;
- return 0;
+ theSurf->D2 (theUV.X(), theUV.Y(), aDummyPnt, DU, DV, D2U, D2V, D2UV);
+ CSLib::Normal (DU, DV, D2U, D2V, D2UV, theTol, isDone, aStatus, aNormal);
+ if (!isDone)
+ {
+ // computation is impossible
+ return aStatus == CSLib_D1NIsNull ? 2 : 3;
}
- else {
- gp_Vec D2U, D2V, D2UV;
- Standard_Boolean isDone;
- CSLib_NormalStatus aStatus;
- gp_Dir aNormal;
-
- S->D2(UV.X(), UV.Y(), DummyPnt, DU, DV, D2U, D2V, D2UV);
- CSLib::Normal(DU, DV, D2U, D2V, D2UV, Tol, isDone, aStatus, aNormal);
-
- if (isDone) {
- Standard_Real Umin, Umax, Vmin, Vmax;
- Standard_Real step = 1.0e-5;
- Standard_Real eps = 1.0e-16;
- Standard_Real sign = -1.0;
-
- S->Bounds(Umin, Umax, Vmin, Vmax);
-
- // check for cone apex singularity point
- if ((UV.Y() > Vmin + step) && (UV.Y() < Vmax - step))
- {
- gp_Dir aNormal1, aNormal2;
- Standard_Real aConeSingularityAngleEps = 1.0e-4;
- S->D1(UV.X(), UV.Y() - sign * step, DummyPnt, DU, DV);
- if ((DU.XYZ().SquareModulus() > eps) && (DV.XYZ().SquareModulus() > eps)) {
- aNormal1 = DU^DV;
- S->D1(UV.X(), UV.Y() + sign * step, DummyPnt, DU, DV);
- if ((DU.XYZ().SquareModulus() > eps) && (DV.XYZ().SquareModulus() > eps)) {
- aNormal2 = DU^DV;
- if (aNormal1.IsOpposite(aNormal2, aConeSingularityAngleEps))
- return 2;
- }
- }
- }
- // Along V
- if(MDU < aTol2 && MDV >= aTol2) {
- if ((Vmax - UV.Y()) > (UV.Y() - Vmin))
- sign = 1.0;
- S->D1(UV.X(), UV.Y() + sign * step, DummyPnt, DU, DV);
- gp_Vec Norm = DU^DV;
- if (Norm.SquareMagnitude() < eps) {
- Standard_Real sign1 = -1.0;
- if ((Umax - UV.X()) > (UV.X() - Umin))
- sign1 = 1.0;
- S->D1(UV.X() + sign1 * step, UV.Y() + sign * step, DummyPnt, DU, DV);
- Norm = DU^DV;
- }
- if ((Norm.SquareMagnitude() >= eps) && (Norm.Dot(aNormal) < 0.0))
- aNormal.Reverse();
- }
+ Standard_Real Umin, Umax, Vmin, Vmax;
+ Standard_Real step = 1.0e-5;
+ Standard_Real eps = 1.0e-16;
+ Standard_Real sign = -1.0;
+ theSurf->Bounds (Umin, Umax, Vmin, Vmax);
- // Along U
- if(MDV < aTol2 && MDU >= aTol2) {
- if ((Umax - UV.X()) > (UV.X() - Umin))
- sign = 1.0;
- S->D1(UV.X() + sign * step, UV.Y(), DummyPnt, DU, DV);
- gp_Vec Norm = DU^DV;
- if (Norm.SquareMagnitude() < eps) {
- Standard_Real sign1 = -1.0;
- if ((Vmax - UV.Y()) > (UV.Y() - Vmin))
- sign1 = 1.0;
- S->D1(UV.X() + sign * step, UV.Y() + sign1 * step, DummyPnt, DU, DV);
- Norm = DU^DV;
- }
- if ((Norm.SquareMagnitude() >= eps) && (Norm.Dot(aNormal) < 0.0))
- aNormal.Reverse();
- }
+ // check for cone apex singularity point
+ if ((theUV.Y() > Vmin + step)
+ && (theUV.Y() < Vmax - step))
+ {
+ gp_Dir aNormal1, aNormal2;
+ Standard_Real aConeSingularityAngleEps = 1.0e-4;
+ theSurf->D1(theUV.X(), theUV.Y() - sign * step, aDummyPnt, DU, DV);
+ if ((DU.XYZ().SquareModulus() > eps) && (DV.XYZ().SquareModulus() > eps))
+ {
+ aNormal1 = DU ^ DV;
+ theSurf->D1 (theUV.X(), theUV.Y() + sign * step, aDummyPnt, DU, DV);
+ if ((DU.XYZ().SquareModulus() > eps)
+ && (DV.XYZ().SquareModulus() > eps))
+ {
+ aNormal2 = DU^DV;
+ if (aNormal1.IsOpposite (aNormal2, aConeSingularityAngleEps))
+ {
+ return 2;
+ }
+ }
+ }
+ }
+
+ // Along V
+ if (MDU < aTol2
+ && MDV >= aTol2)
+ {
+ if ((Vmax - theUV.Y()) > (theUV.Y() - Vmin))
+ {
+ sign = 1.0;
+ }
- // quasysingular
- if ((aStatus == CSLib_D1NuIsNull) || (aStatus == CSLib_D1NvIsNull) ||
- (aStatus == CSLib_D1NuIsParallelD1Nv)) {
- N.SetXYZ(aNormal.XYZ());
- return 1;
+ theSurf->D1 (theUV.X(), theUV.Y() + sign * step, aDummyPnt, DU, DV);
+ gp_Vec Norm = DU ^ DV;
+ if (Norm.SquareMagnitude() < eps)
+ {
+ Standard_Real sign1 = -1.0;
+ if ((Umax - theUV.X()) > (theUV.X() - Umin))
+ {
+ sign1 = 1.0;
}
- // conical
- if (aStatus == CSLib_InfinityOfSolutions)
- return 2;
+ theSurf->D1 (theUV.X() + sign1 * step, theUV.Y() + sign * step, aDummyPnt, DU, DV);
+ Norm = DU ^ DV;
}
- // computation is impossible
- else {
- // conical
- if (aStatus == CSLib_D1NIsNull) {
- return 2;
+ if (Norm.SquareMagnitude() >= eps
+ && Norm.Dot (aNormal) < 0.0)
+ {
+ aNormal.Reverse();
+ }
+ }
+
+ // Along U
+ if (MDV < aTol2
+ && MDU >= aTol2)
+ {
+ if ((Umax - theUV.X()) > (theUV.X() - Umin))
+ {
+ sign = 1.0;
+ }
+
+ theSurf->D1 (theUV.X() + sign * step, theUV.Y(), aDummyPnt, DU, DV);
+ gp_Vec Norm = DU ^ DV;
+ if (Norm.SquareMagnitude() < eps)
+ {
+ Standard_Real sign1 = -1.0;
+ if ((Vmax - theUV.Y()) > (theUV.Y() - Vmin))
+ {
+ sign1 = 1.0;
}
- return 3;
+
+ theSurf->D1 (theUV.X() + sign * step, theUV.Y() + sign1 * step, aDummyPnt, DU, DV);
+ Norm = DU ^ DV;
+ }
+ if (Norm.SquareMagnitude() >= eps
+ && Norm.Dot (aNormal) < 0.0)
+ {
+ aNormal.Reverse();
}
}
- return 3;
+
+ // quasysingular
+ if (aStatus == CSLib_D1NuIsNull
+ || aStatus == CSLib_D1NvIsNull
+ || aStatus == CSLib_D1NuIsParallelD1Nv)
+ {
+ theNorm.SetXYZ (aNormal.XYZ());
+ return 1;
+ }
+
+ return aStatus == CSLib_InfinityOfSolutions ? 2 : 3;
}
//=======================================================================
projects / occt.git / commitdiff