/****************************************************************************** * CagdSRev.c - Surface of revolution out of a given profile. * ******************************************************************************* * (C) Gershon Elber, Technion, Israel Institute of Technology * ******************************************************************************* * Written by Gershon Elber, Mar. 91. * ******************************************************************************/ #include "cagd_loc.h" static int CircRationalKnotVector[12] = { 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4 }, CircPolynomialKnotVector[17] = { 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4 }; static CagdRType PolyApproxRotAngles[] = { 0, 33.523898, /* arcsin(4 (sqrt(2) - 1) / 3) */ 90 - 33.523898, 90 }; /***************************************************************************** * DESCRIPTION: M * Constructs a surface of revolution around the Z axis of the given profile M * curve. Resulting surface will be a Bspline surface, while input may be M * either a Bspline or a Bezier curve. M * * * PARAMETERS: M * Crv: To create surface of revolution around Z with. M * * * RETURN VALUE: M * CagdSrfStruct *: Surface of revolution. M * * * KEYWORDS: M * CagdSurfaceRev, surface of revolution, surface constructors M *****************************************************************************/ CagdSrfStruct *CagdSurfaceRev(CagdCrvStruct *Crv) { int i, j, i9, Len = Crv -> Length; CagdPointType PType = Crv -> PType; CagdRType **SrfPoints, sin45 = sin(M_PI / 4.0), **CrvPoints = Crv -> Points; CagdSrfStruct *Srf = BspPeriodicSrfNew(9, Len, 3, Crv -> Order, FALSE, Crv -> Periodic, CAGD_PT_P3_TYPE); for (i = 0; i < 12; i++) Srf -> UKnotVector[i] = (CagdRType) CircRationalKnotVector[i]; switch (Crv -> GType) { case CAGD_CBEZIER_TYPE: BspKnotUniformOpen(Len, Crv -> Order, Srf -> VKnotVector); break; case CAGD_CBSPLINE_TYPE: CAGD_GEN_COPY(Srf -> VKnotVector, Crv -> KnotVector, sizeof(CagdRType) * (CAGD_CRV_PT_LST_LEN(Crv) + Crv -> Order)); break; case CAGD_CPOWER_TYPE: CAGD_FATAL_ERROR(CAGD_ERR_POWER_NO_SUPPORT); return NULL; default: CAGD_FATAL_ERROR(CAGD_ERR_UNDEF_CRV); return NULL; } SrfPoints = Srf -> Points; /* For each control point in the original curve - generate 9 points that */ /* Form a circle perpendicular to the Z axis. */ for (i = i9 = 0; i < Len; i++, i9 += 9) { SrfPoints[W][i9] = 1.0; switch (PType) { case CAGD_PT_P3_TYPE: SrfPoints[W][i9] = CrvPoints[W][i]; case CAGD_PT_E3_TYPE: SrfPoints[X][i9] = CrvPoints[X][i]; SrfPoints[Y][i9] = CrvPoints[Y][i]; SrfPoints[Z][i9] = CrvPoints[Z][i]; break; default: CAGD_FATAL_ERROR(CAGD_ERR_UNSUPPORT_PT); break; } /* Last point is exactly the same as first one in circle - copy it. */ for (j = W; j <= Z; j++) SrfPoints[j][i9 + 8] = SrfPoints[j][i9]; /* The Z components are identical in all circle, while the XY */ /* components are rotated 45 degrees at a time: */ for (j = 1; j < 8; j++) { SrfPoints[W][i9 + j] = SrfPoints[W][i9]; SrfPoints[X][i9 + j] = SrfPoints[X][i9 + j - 1] * sin45 - SrfPoints[Y][i9 + j - 1] * sin45; SrfPoints[Y][i9 + j] = SrfPoints[X][i9 + j - 1] * sin45 + SrfPoints[Y][i9 + j - 1] * sin45; SrfPoints[Z][i9 + j] = SrfPoints[Z][i9]; } /* And finally we need to compensate for the W's on every second pt. */ for (j = 1; j < 8; j += 2) { SrfPoints[W][i9 + j] *= sin45; SrfPoints[Z][i9 + j] *= sin45; } } return Srf; } /***************************************************************************** * DESCRIPTION: M * Constructs a surface of revolution around the Z axis of the given profile M * curve. Resulting surface will be a Bspline surface, while input may be M * either a Bspline or a Bezier curve. M * Resulting surface will be a polynomial Bspline surface, approximating a M * surface of revolution using a polynomial circle approx. M * (See Faux & Pratt "Computational Geometry for Design and Manufacturing"). M * * * PARAMETERS: M * Crv: To approximate a surface of revolution around Z with. M * * * RETURN VALUE: M * CagdSrfStruct *: Surface of revolution approximation. M * * * KEYWORDS: M * CagdSurfaceRevPolynomialApprox, surface of revolution, surface M * constructors M *****************************************************************************/ CagdSrfStruct *CagdSurfaceRevPolynomialApprox(CagdCrvStruct *Crv) { int i, j, i13, Len = Crv -> Length; CagdPointType PType = Crv -> PType; CagdRType **SrfPoints, **CrvPoints = Crv -> Points; CagdSrfStruct *Srf = BspPeriodicSrfNew(13, Len, 4, Crv -> Order, FALSE, Crv -> Periodic, CAGD_PT_E3_TYPE); if (CAGD_IS_RATIONAL_CRV(Crv)) { CAGD_FATAL_ERROR(CAGD_ERR_POLYNOMIAL_EXPECTED); return NULL; } for (i = 0; i < 17; i++) Srf -> UKnotVector[i] = (CagdRType) CircPolynomialKnotVector[i]; switch (Crv -> GType) { case CAGD_CBEZIER_TYPE: BspKnotUniformOpen(Len, Crv -> Order, Srf -> VKnotVector); break; case CAGD_CBSPLINE_TYPE: CAGD_GEN_COPY(Srf -> VKnotVector, Crv -> KnotVector, sizeof(CagdRType) * (CAGD_CRV_PT_LST_LEN(Crv) + Crv -> Order)); break; case CAGD_CPOWER_TYPE: CAGD_FATAL_ERROR(CAGD_ERR_POWER_NO_SUPPORT); return NULL; default: CAGD_FATAL_ERROR(CAGD_ERR_UNDEF_CRV); return NULL; } SrfPoints = Srf -> Points; /* For each control point in original curve - generate 13 points that */ /* Form a circle approximation) perpendicular to the Z axis. */ for (i = i13 = 0; i < Len; i++, i13 += 13) { int Quad; switch (PType) { case CAGD_PT_E3_TYPE: SrfPoints[X][i13] = sqrt(SQR(CrvPoints[X][i]) + SQR(CrvPoints[Y][i])); SrfPoints[Y][i13] = 0.0; SrfPoints[Z][i13] = CrvPoints[Z][i]; break; default: CAGD_FATAL_ERROR(CAGD_ERR_UNSUPPORT_PT); break; } /* Last point is exactly the same as first one in circle - copy it. */ for (j = X; j <= Z; j++) SrfPoints[j][i13 + 12] = SrfPoints[j][i13]; /* The Z components are identical in all circle, while the XY */ /* components are functions of PolyApproxRotAngles: */ for (Quad = 0, j = 1; j < 12; j++) { CagdRType Angle, CosAngle, SinAngle; if (j % 3 == 0) Quad++; Angle = Quad * 90 + PolyApproxRotAngles[j % 3]; CosAngle = cos(DEG2RAD(Angle)); SinAngle = sin(DEG2RAD(Angle)); if (ABS(CosAngle) > ABS(SinAngle)) CosAngle /= ABS(CosAngle); else SinAngle /= ABS(SinAngle); SrfPoints[X][i13 + j] = SrfPoints[X][i13] * CosAngle; SrfPoints[Y][i13 + j] = SrfPoints[X][i13] * SinAngle; SrfPoints[Z][i13 + j] = SrfPoints[Z][i13]; } } return Srf; }