impl of helix & TBN for articulation of polylines

.clang-tidy

@@ -5,6 +5,8 @@ Checks: "
   			performance-*,
   			readability-*,
         -readability-braces-around-statements,
+        -readability-magic-numbers,
+        -readability-identifier-length,
   			misc-*,
         -misc-non-private-member-variables-in-classes,
         clang-analyzer-*,
@@ -15,7 +17,7 @@ Checks: "
   			performance-unnecessary-value-param,
   			modernize-pass-by-value,
 
-				-readability-identifier-length,
+
         -modernize-use-trailing-return-type,
         -cppcoreguidelines-magic-numbers,
 				-cppcoreguidelines-init-variables,

include/common.hpp

@@ -2,13 +2,19 @@
 #include "real.hpp"
 #include <limits>
 #include <numbers>
+#include <cmath>
 
 enum PtBoundaryRelation { Inside = -1, OnBoundary, Outside = 1 };
 
 const real PI = std::numbers::pi;
 const real PI2 = 2 * PI;
 const real EPS = std::numeric_limits<real>::epsilon() * 1e2;
-inline bool isEqual(double a, double b) {
-    // TODO
-    return a == b;
+const real EPS_NEWTON_ITERATION = std::numeric_limits<real>::epsilon() * 1e6;
+
+const real HALF = 0.5;
+const real ONE_FOURTH = 0.25;
+const real ONE_EIGHT = 0.125;
+
+inline bool isEqual(real a, real b) {
+    return fabs(a - b) < EPS;
 }

include/line.hpp

@@ -1,12 +1,15 @@
 #pragma once
 
 #include "common.hpp"
+#include "real.hpp"
 #include "vec.hpp"
 #include <algorithm>
 #include <cassert>
 #include <cmath>
+#include <cstddef>
 #include <iostream>
 #include <limits.h>
+#include <limits>
 #include <memory>
 #include <numbers>
 #include <vector>
@@ -31,7 +34,7 @@ struct ClosestDescOnSeg {
     ClosestDescOnSeg(real _t, real _dis) : t(_t), dis(_dis) {}
     ClosestDescOnSeg() : t(0), dis(std::numeric_limits<real>::max()) {}
 };
-
+// vscode C++ override跳转插件
 class ILine {
 public:
     int aaa;
@@ -44,6 +47,8 @@ public:
     virtual Vec3 der2(real param) = 0;
 
     virtual ClosestDescOnSeg getClosestParam(const Vec3 &p) = 0;
+
+    [[nodiscard]] virtual bool isEndParam(real t) const = 0;
 };
 
 template <typename VecType> // Vec2 or Vec3
@@ -111,11 +116,11 @@ public:
         for (size_t i = 0; i < _bugles.size(); ++i) {
             const Point &A = _points[i];
             const Point &B = _points[(i + 1) % _points.size()];
-            Vec3 ABHalf = (B - A) * 0.5;
+            Vec3 ABHalf = (B - A) * HALF;
             Vec3 ABNorm = ABHalf.normalize();
             real theta = std::atan(_bugles[i]) * 4;
-            circularArcs[i].inCircleDir = _normal.cross(ABNorm) * (abs(_bugles[i]) > 1 ? -1 : 1);
-            circularArcs[i].h = ABHalf.norm() * std::tan(theta * 0.5);
+            circularArcs[i].inCircleDir = _normal.cross(ABNorm) * (fabs(_bugles[i]) > 1 ? -1 : 1);
+            circularArcs[i].h = ABHalf.norm() * std::tan(theta * HALF);
             circularArcs[i].center = A + ABHalf + circularArcs[i].inCircleDir * circularArcs[i].h;
             circularArcs[i].theta = theta;
             circularArcs[i].radius = (circularArcs[i].center - A).norm();
@@ -290,23 +295,123 @@ public:
         return {h, (AP - AB * h).norm()};
     }
 
-    bool isEndParm(real t) { return t < EPS || t > _points.size() - 1 - EPS; }
+    [[nodiscard]] bool isEndParam(real t) const override {
+        return t < EPS || t > static_cast<real>(_bugles.size()) - EPS;
+    }
 };
 
 class HelixLine : public ILine {
 public:
-    Vec3 eval(real param) override { return {}; };
+    HelixLine(const Vec3 &axisStart, const Vec3 &axisEnd, real r, real advancePerRound,
+              const Vec3 &startDir)
+        : _axisStart(axisStart), _frequency(PI2 / advancePerRound), _u(startDir), _r(r),
+          _2pir_p(PI2 * _r / advancePerRound), _4pi2r_p2(_2pir_p * PI2 / advancePerRound),
+          SEG_T(advancePerRound / SEG_PER_ROUND), SEG_T_HALF(SEG_T / 2) {
+        auto star2nd = axisEnd - _axisStart;
+        _advanceLen = star2nd.norm();
+        _axisDir = star2nd / _advanceLen;
+        _v = _axisDir.cross(_u);
+        real _4pi2r = PI2 * PI2 * _r;
+        // _k = _4pi2r / (advancePerRound * advancePerRound + _4pi2r * _r);
+        _arcDeltaMaxFactor = _4pi2r / (advancePerRound * advancePerRound + _4pi2r * _r) * ONE_EIGHT;
+    }
+    Vec3 eval(real t) override {
+        real theta = _frequency * t;
+        return _axisStart + _axisDir * t + (_u * std::cos(theta) + _v * std::sin(theta)) * _r;
+    };
 
-    Vec3 der1(real param) override { return {}; };
+    Vec3 der1(real param) override {
+        real theta = _frequency * param;
+        return _axisDir + _2pir_p * (_v * std::cos(theta) - _u * std::sin(theta));
+    };
 
-    Vec3 der2(real param) override { return {}; };
+    Vec3 der2(real param) override {
+        real theta = _frequency * param;
+        return -_4pi2r_p2 * (_u * std::cos(theta) + _v * std::sin(theta));
+    };
 
-    ClosestDescOnSeg getClosestParam(const Vec3 &p) override { return {}; };
+    ClosestDescOnSeg getClosestParam(const Vec3 &p) override {
+        // discretization and traversal
+        real startT = 0;
+        real endT = SEG_T;
+        auto segCount = static_cast<size_t>(std::ceil(_advanceLen / SEG_T));
+        std::vector<ClosestDescOnSeg> sampledSegs(segCount + 2); // 加上首尾
+        std::vector<Vec3> samplePoints(segCount + 2);
+
+        ClosestDescOnSeg closestSampleDes;
+        for (size_t i = 0; i < segCount; ++i, startT = endT, endT += SEG_T) {
+            real sampledT = fmin(startT + SEG_T_HALF, _advanceLen);
+            samplePoints[i] = eval(sampledT);
+            sampledSegs[i].dis = (samplePoints[i] - p).norm();
+            sampledSegs[i].t = sampledT;
+            if (sampledSegs[i].dis < closestSampleDes.dis) {
+                closestSampleDes = sampledSegs[i];
+            }
+        }
+        // 特别考虑两端，因为有更多的情形，查询点会离两端更近
+        // 好处是可能降低后续迭代次数
+        samplePoints[segCount] = eval(0);
+        samplePoints[segCount + 1] = eval(_advanceLen);
+        sampledSegs[segCount] = {0, (samplePoints[segCount] - p).norm()};
+        sampledSegs[segCount + 1] = {_advanceLen, (samplePoints[segCount + 1] - p).norm()};
+        for (size_t i = segCount; i <= segCount + 1; ++i) {
+            if (sampledSegs[i].dis < closestSampleDes.dis) {
+                closestSampleDes = sampledSegs[i];
+            }
+        }
+
+        real deltaMaxCommon = (eval(0) - eval(SEG_T)).l2() * _arcDeltaMaxFactor;
+        for (int i = 0; i < sampledSegs.size(); ++i) {
+            if (i == segCount - 1) {
+                // 最后一段
+                deltaMaxCommon =
+                    (eval(_advanceLen) - eval(SEG_T * static_cast<real>(segCount - 1))).l2()
+                    * _arcDeltaMaxFactor;
+            } else if (i == segCount || i == segCount + 1) {
+                // 首尾点
+                deltaMaxCommon = 0;
+            }
+            if (sampledSegs[i].dis - deltaMaxCommon < closestSampleDes.dis) {
+                Vec3 q = samplePoints[i];
+                real t = sampledSegs[i].t;
+                Vec3 qDer1 = der1(t);
+                Vec3 qDer2 = der2(t);
+                real lDer1 = (q - p).dot(qDer1);
+                int iter = 0;
+                while (fabs(lDer1) > EPS_NEWTON_ITERATION) {
+                    real dif = lDer1 / (qDer1.dot(qDer1) + (q - p).dot(qDer2));
+                    real tNew = t - dif;
+                    if (tNew < 0 || tNew > _advanceLen)
+                        break;
+                    t = tNew;
+                    q = eval(t);
+                    qDer1 = der1(t);
+                    qDer2 = der2(t);
+                    lDer1 = (q - p).dot(qDer1);
+                    std::cout << "After iter " << iter << ", dL is " << lDer1 << std::endl;
+                    iter++;
+                }
+                real dis = (q - p).norm();
+                if (dis < closestSampleDes.dis) {
+                    closestSampleDes = {t, dis};
+                }
+            }
+        }
+        return closestSampleDes;
+    };
+
+    [[nodiscard]] bool isEndParam(real t) const override {
+        return t < EPS || t > _advanceLen - EPS;
+    }
 
 private:
-    Vec3 axisStart, axisDir;
-    real advanceLen, advancePerRound;
-    real startTheta; // 轴线起始时在螺旋投影（圆）上的参数
+    Vec3 _axisStart, _axisDir;
+    real _advanceLen, _frequency;
+    real _startTheta;
+    Vec3 _u, _v; // 螺旋投影圆面上的两个正交单位向量，u X v = axisDir
+    real _r, _2pir_p, _4pi2r_p2, _arcDeltaMaxFactor;
+    const int SEG_PER_ROUND = 12;
+    const real SEG_T, SEG_T_HALF;
 };
 
 class SingleLine : public ILine {

include/solid.hpp

@@ -2,6 +2,7 @@
 
 #include "common.hpp"
 #include "real.hpp"
+#include <array>
 #include <cassert>
 #include <cstddef>
 #include <utility>
@@ -22,12 +23,18 @@ inline Vec2 get2DRepOf3DPt(const Vec3 &pt3D, const Vec3 &u, const Vec3 &v, const
 inline Vec2 get2DRepOf3DDir(const Vec3 &dir, const Vec3 &u, const Vec3 &v) {
     return Vec2{dir.dot(u), dir.dot(v)}.normalize();
 }
-class IExtrudedSolid : public ISolid {
-public:
+
+template <typename AxisLineType>
+class IExtrudedSolidBase : public ISolid {
+protected:
     std::vector<Polyline> _profiles; // TODO: may be replaced by const ref to profile
+    AxisLineType _axis;
     real _rScale;
-    IExtrudedSolid(std::vector<Polyline> profiles, real rScale)
-        : _profiles(std::move(profiles)), _rScale(rScale) {}
+    IExtrudedSolidBase(std::vector<Polyline> profiles, AxisLineType axis, real rScale)
+        : _profiles(std::move(profiles)), _axis(std::move(axis)), _rScale(rScale) {}
+
+public:
+    virtual real sdf(const Vec3 &p) = 0;
 };
 
 /**
@@ -42,25 +49,26 @@ public:
 //            / (std::numbers::pi * 2);
 // }
 
-class ExtrudedSolidPolyline : public IExtrudedSolid {
+// template <typename AxisLineType>
+class ExtrudedSolidPolyline : public IExtrudedSolidBase<Polyline> {
 private:
-    Polyline _axis;
     std::vector<Pt2Array> _localProfiles2D;
     std::vector<std::vector<CircularArc<Vec2>>> _localArcs2d;
-    // Pt2Array _localCircleCenter2D;
-    // Pt2Array _localInCircleDir;
+    Vec3 _biNormal;
+
 public:
     ExtrudedSolidPolyline(std::vector<Polyline> profiles, Polyline axis, real rScale)
-        : IExtrudedSolid(std::move(profiles), rScale), _axis(std::move(axis)) {
+        : IExtrudedSolidBase(std::move(profiles), std::move(axis), rScale) {
         assert(!_profiles.empty());
         for (const auto &_profile : _profiles) {
             assert(_profile.isClosed());
         }
-        // TODO: project profile at st point to 2D
-        Vec3 T = _axis.der1(0).normalize();
-        Vec3 N = _axis.der2(0).normalize();
-        Vec3 B = T.cross(N);
-        Vec3 Q = _axis.eval(0);
+        // project profile at st point to 2D
+        Vec3 tangent = _axis.der1(0).normalize();
+        Vec3 normal = _axis.der2(0).normalize();
+        _biNormal = tangent.cross(normal);
+        assert(_biNormal.isParallel(_axis.getNormal()));
+        Vec3 q = _axis.eval(0);
         size_t profileCount = _profiles.size();
         _localProfiles2D.resize(profileCount);
         _localArcs2d.resize(profileCount);
@@ -71,11 +79,12 @@ public:
             _localArcs2d[i].resize(segCount);
             for (int j = 0; j < segCount; ++j) {
                 // TODO:
-                _localProfiles2D[i][j] = get2DRepOf3DPt(profile.getPoints()[j] - Q, N, B, Q);
+                _localProfiles2D[i][j] =
+                    get2DRepOf3DPt(profile.getPoints()[j] - q, normal, _biNormal, q);
                 auto &arc2d = _localArcs2d[i][j];
                 const auto &arc3d = profile.getCircularArcs()[j];
-                arc2d.center = get2DRepOf3DPt(arc3d.center - Q, N, B, Q);
-                arc2d.inCircleDir = get2DRepOf3DDir(arc3d.inCircleDir, N, B);
+                arc2d.center = get2DRepOf3DPt(arc3d.center - q, normal, _biNormal, q);
+                arc2d.inCircleDir = get2DRepOf3DDir(arc3d.inCircleDir, normal, _biNormal);
                 arc2d.radius = arc3d.radius;
                 arc2d.theta = arc3d.theta;
                 arc2d.h = arc3d.h;
@@ -87,52 +96,81 @@ public:
         ClosestDescOnSeg closestDescToAxis = _axis.getClosestParam(p);
         // TNB coordinate system
         auto t = closestDescToAxis.t;
-        Vec3 Q = _axis.eval(t); // closest point on axis
-        Vec3 QP = p - Q;
-        Vec3 T = _axis.der1(t).normalize();
-        if (_axis.isEndParm(t) && fabs(QP.dot(T)) > EPS) {
+        Vec3 q = _axis.eval(t); // closest point on axis
+        Vec3 qp = p - q;
+        auto TBN = getTBN(p, q, closestDescToAxis);
+        const Vec3 &tangent = TBN[0];
+        const Vec3 &normal = TBN[1];
+        const Vec3 &biNormal = TBN[2];
+        if (_axis.isEndParam(t) && fabs(qp.dot(tangent)) > EPS) {
             // project p to the plane passing through Q and perpendicular to T
-            Vec3 projP = p + T * (-QP.dot(T));
+            real pqDotT = -qp.dot(tangent);
+            Vec3 projP = p + tangent * pqDotT;
+            Vec2 p2D = get2DRepOf3DPt(projP, normal, biNormal, q);
+            PtBoundaryRelation ptProfileRelation = pmcProfile2d(p2D);
+            real projectedDis = 0;
+            if (ptProfileRelation == Outside)
+                projectedDis = disProfile2D(p2D).dis;
+            // must be positive (outside)
+            return sqrt(projectedDis * projectedDis + pqDotT * pqDotT);
         }
 
-        Vec3 N = _axis.der2(t).normalize();
-        Vec3 B = T.cross(N);
+        Vec2 p2D = get2DRepOf3DPt(p, normal, biNormal, q);
+        PtBoundaryRelation ptProfileRelation = pmcProfile2d(p2D);
+        if (ptProfileRelation == OnBoundary)
+            return 0;
+        auto closestDescToProfile = disProfile2D(p2D);
+        return closestDescToProfile.dis * static_cast<int>(ptProfileRelation);
+    }
 
-        auto p2D = get2DRepOf3DPt(QP, N, B, Q);
-        // PMC
-        PtBoundaryRelation ptProfileRelation = Inside;
-        for (int i = 0; i < _localArcs2d.size(); ++i) {
-            PtBoundaryRelation relationTmp =
-                getPtProfileRelation(p2D, _localProfiles2D[i], _localArcs2d[i]);
-            if (relationTmp == OnBoundary) {
-                return 0; // TODO: 判断OnBoundary的过程可以加一点容差
+    std::array<Vec3, 3> getTBN(const Vec3 &p, const Vec3 &q, const ClosestDescOnSeg &closestDesc) {
+        real t = closestDesc.t;
+        if (std::abs(t - std::round(t)) < EPS) {
+            // 端点处
+            // p到圆弧平面的投影
+            Vec3 projPt = p - _biNormal.dot(p - q) * _biNormal;
+            Vec3 normal = (q - projPt).normalize();
+            if (normal.dot(_axis.der2(t)) < 0) {
+                normal = -normal;
             }
-            if ((relationTmp == Outside && i == 0) || (relationTmp == Inside && i != 0)) {
-                ptProfileRelation = Outside;
-                break;
+            return {normal.cross(_biNormal), normal, _biNormal};
         }
+        return {_axis.der1(t).normalize(), _axis.der1(t).normalize(), _biNormal};
     }
 
-        // distance
+private:
+    inline ClosestDescOnSeg disProfile2D(const Vec2 &p2D) {
         ClosestDescOnSeg closestDescToProfile{};
         for (int i = 0; i < _localArcs2d.size(); ++i) {
-            ClosestDescOnSeg closestDescTemp =
-                distance2Profile2D(p2D, _localProfiles2D[i], _localArcs2d[i]);
+            ClosestDescOnSeg closestDescTemp = disLoop2D(p2D, _localProfiles2D[i], _localArcs2d[i]);
             if (closestDescTemp.dis < closestDescToProfile.dis) {
                 closestDescToProfile = closestDescTemp;
             }
         }
-        return closestDescToProfile.dis * static_cast<int>(ptProfileRelation);
+        return closestDescToProfile;
     }
 
-private:
-    /** 低于2Dprofile的内外部判定
+    inline PtBoundaryRelation pmcProfile2d(const Vec2 &p2D) {
+        // PMC
+        for (int i = 0; i < _localArcs2d.size(); ++i) {
+            PtBoundaryRelation relationTmp = pmcLoop2d(p2D, _localProfiles2D[i], _localArcs2d[i]);
+            if (relationTmp == OnBoundary) {
+                return OnBoundary; // TODO: 判断OnBoundary的过程可以加一点容差
+            }
+            if ((relationTmp == Outside && i == 0) || (relationTmp == Inside && i != 0)) {
+                return Outside;
+            }
+        }
+        return Inside;
+    }
+
+    /** 2D Loop的内外部判定
      * in + in = out
      * in + out = in
      * out + in = in
      * out + out = out
      */
-    static PtBoundaryRelation getPtProfileRelation(const Vec2 &p2D, const Pt2Array &profile2D,
+    static PtBoundaryRelation pmcLoop2d(const Vec2 &p2D, const Pt2Array &loop2D,
                                         const std::vector<CircularArc<Vec2>> &arcs2d) {
         size_t segCount = arcs2d.size();
         // 先判断是否在outline上
@@ -140,8 +178,8 @@ private:
         bool inFan = false;
         int onLinesegButHasBugle = -1;
         for (int i = 0; i < segCount; ++i) {
-            const Vec2 &a = profile2D[i];
-            const Vec2 &b = profile2D[(i + 1) % segCount];
+            const Vec2 &a = loop2D[i];
+            const Vec2 &b = loop2D[(i + 1) % segCount];
             if (arcs2d[i].h <= EPS) {
                 //straight line segment
                 if (isPointOnSegment(p2D, a, b)) {
@@ -184,8 +222,8 @@ private:
                 int crossings = 0;
 
                 for (int i = 0; i < segCount; ++i) {
-                    const Vec2 &a = profile2D[i];
-                    const Vec2 &b = profile2D[(i + 1) % segCount];
+                    const Vec2 &a = loop2D[i];
+                    const Vec2 &b = loop2D[(i + 1) % segCount];
                     assert(isPointOnSegment(p, a, b));
                     // if (isPointOnSegment(p2D, a, b))
                     // {
@@ -229,14 +267,13 @@ private:
         return ptInPolygon(p2D) ^ inFan ? Inside : Outside;
     }
 
-    static ClosestDescOnSeg distance2Profile2D(const Vec2 &p2D, const Pt2Array &profile2D,
+    static ClosestDescOnSeg disLoop2D(const Vec2 &p2D, const Pt2Array &loop2D,
                                       const std::vector<CircularArc<Vec2>> &arcs2d) {
         size_t segCount = arcs2d.size();
-        assert(profile2D.size() == segCount);
+        assert(loop2D.size() == segCount);
         ClosestDescOnSeg res{};
         for (int i = 0; i < segCount; ++i) {
-            auto disDesc =
-                distance2Arc2D(p2D, profile2D[i], profile2D[(i + 1) % segCount], arcs2d[i]);
+            auto disDesc = distance2Arc2D(p2D, loop2D[i], loop2D[(i + 1) % segCount], arcs2d[i]);
             if (res.dis > disDesc.dis) {
                 res.dis = disDesc.dis;
                 res.t = i + disDesc.t;
@@ -330,8 +367,3 @@ private:
     //     return arc.center + arc.radius * (arc.u * std::cos(phi) + arc.v * std::sin(phi));
     // }
 };
-
-class ExtrudedSolidPolynomialLine : public IExtrudedSolid {
-protected:
-    PolynomialLine _axis;
-};

include/vec.hpp

@@ -1,5 +1,6 @@
 #pragma once
 
+#include "common.hpp"
 #include "real.hpp"
 #include <cmath>
 #include <array>
@@ -19,13 +20,15 @@ public:
         std::copy(values.begin(), values.end(), data.begin());
     }
 
+    VecBase(real v) : data{v} {}
+
+    VecBase(const VecBase &v) : data(v.data) {}
+
     template <typename... Args>
     explicit VecBase(Args... args) : data{static_cast<real>(args)...} {
         static_assert(sizeof...(args) == N, "Argument count must match vector size.");
     }
 
-    explicit VecBase(const VecBase &v) { data = v.data; }
-
     VecBase &operator=(VecBase v) {
         *this = std::move(v);
         return *this;
@@ -93,9 +96,21 @@ public:
 
     real norm() const { return std::sqrt(dot(*this)); }
 
+    real l2() const { return dot(*this); }
+
     Derived normalize() const { return static_cast<Derived>(*this / norm()); }
 
     Derived reflect(const Derived &n) const { return static_cast<Derived>(*this - n * 2 * dot(n)); }
+
+    bool operator==(const VecBase &v) const {
+        for (size_t i = 0; i < N; ++i) {
+            if (!isEqual(data[i], v[i]))
+                return false;
+        }
+        return true;
+    }
+
+    Derived operator-() const { return static_cast<Derived>(*this * -1); }
 };
 
 // Vec<2> 特化
@@ -113,16 +128,16 @@ public:
     real &x() { return data[0]; }
     real &y() { return data[1]; }
 
-    const real &x() const { return data[0]; }
-    const real &y() const { return data[1]; }
+    [[nodiscard]] const real &x() const { return data[0]; }
+    [[nodiscard]] const real &y() const { return data[1]; }
 
     real &u() { return data[0]; }
     real &v() { return data[1]; }
 
-    const real &u() const { return data[0]; }
-    const real &v() const { return data[1]; }
+    [[nodiscard]] const real &u() const { return data[0]; }
+    [[nodiscard]] const real &v() const { return data[1]; }
 
-    real cross(const Vec2 &v) const { return x() * v.y() - v.x() * y(); }
+    [[nodiscard]] real cross(const Vec2 &v) const { return x() * v.y() - v.x() * y(); }
 };
 
 class Vec3 : public VecBase<Vec3, 3> {
@@ -140,21 +155,23 @@ public:
     real &y() { return data[1]; }
     real &z() { return data[2]; }
 
-    real x() const { return data[0]; }
-    real y() const { return data[1]; }
-    real z() const { return data[2]; }
+    [[nodiscard]] real x() const { return data[0]; }
+    [[nodiscard]] real y() const { return data[1]; }
+    [[nodiscard]] real z() const { return data[2]; }
 
     real &u() { return data[0]; }
     real &v() { return data[1]; }
     real &w() { return data[2]; }
 
-    real u() const { return data[0]; }
-    real v() const { return data[1]; }
-    real w() const { return data[2]; }
+    [[nodiscard]] real u() const { return data[0]; }
+    [[nodiscard]] real v() const { return data[1]; }
+    [[nodiscard]] real w() const { return data[2]; }
 
-    Vec3 cross(const Vec3 &v) const {
+    [[nodiscard]] Vec3 cross(const Vec3 &v) const {
         return {y() * v.z() - z() * v.y(), z() * v.x() - x() * v.z(), x() * v.y() - y() * v.x()};
     }
+
+    [[nodiscard]] bool isParallel(const Vec3 &v) const { return cross(v) == 0; }
 };
 
 using Pt3Array = std::vector<Vec3>;

require.md

@@ -82,15 +82,41 @@ virtual CPmSolid * create_face_helix(const PMSoft::CPMGePoint3DArray &pt3d,
 
 
 
+## 螺旋路径拉伸
+```C++
+virtual CPmSolid * createHelix(const PMSoft::CPMGePoint3DArray &pt3d, 
+	const PmGeDoubleArray bulges, 
+	const PMSoft::CPMGePoint3D &axis_start,
+	const PMSoft::CPMGePoint3D &axis_end,
+	const PMSoft::CPMGeVector3D &start_dir,
+	BOOL handiness,
+	double radius,
+	double pitch);
 
+virtual CPmSolid * createHelix(const PMSoft::CPMGePoint3DArray &pt3d, 
+	const PmGeDoubleArray bulges,
+	const PMSoft::CPMGeVector3D &FaceNormal,
+	const PMSoft::CPMGePoint3D &axis_start,
+	const PMSoft::CPMGePoint3D &axis_end,
+	const PMSoft::CPMGeVector3D &start_dir,
+	BOOL handiness,
+	double radius,
+	double pitch,
+	BOOL bIsFace = FALSE);
 
+virtual CPmSolid * create_face_helix(const PMSoft::CPMGePoint3DArray &pt3d, 
+	const PmGeDoubleArray bulges, 
+	const PMSoft::CPMGePoint3D &axis_start,
+	const PMSoft::CPMGePoint3D &axis_end,
+	const PMSoft::CPMGeVector3D &start_dir,
+	BOOL handiness,
+	double radius,
+	double pitch);
+```
 
 
 
 
-//////////////////////////////////////////////////////////////////////////
-	///                      体生成
-	//////////////////////////////////////////////////////////////////////////
 	// 两截面蒙皮(生成台体)
 	virtual CPmSolid * create_by_faces_to_skin(PmDbPolyline * pStartPoly, PmDbPolyline * pEndPoly, PMSoft::CPMGeVector3D normal/*,BOOL bIsFace*/) override;
 
@@ -104,28 +130,6 @@ virtual CPmSolid * create_face_helix(const PMSoft::CPMGePoint3DArray &pt3d,
 	CPmSolid * create_by_faces_to_skin(const CArray<PMSoft::CPMGePoint3DArray, PMSoft::CPMGePoint3DArray&> &jmsPts3d, const CArray<PmGeDoubleArray, PmGeDoubleArray&> &jmsBulges,
 		const CArray<PMSoft::CPMGeVector3D, PMSoft::CPMGeVector3D&> &normalArr, BOOL bIsFace);
 
-	// 多线段蒙皮(线段不含弧)
-	CPmSolid * createFacesBySkinWithSegs(const CArray<PMSoft::CPMGePoint3DArray, PMSoft::CPMGePoint3DArray&> &segs, BOOL bIsFace);
-
-	virtual CPmSolid * createBox(const PMSoft::CPMGePoint3D& p,double xLen,double yLen,double zLen);
-	virtual CPmSolid * createTorus(const PMSoft::CPMGePoint3D& p, double majorRadius, double minorRadius);
-	virtual CPmSolid * createSphere(const PMSoft::CPMGePoint3D& p, double radius);
-	void CreateCircPoints(int nNum, const PMSoft::CPMGePoint3D& pt, const PMSoft::CPMGePoint3D& ptCent, PMSoft::CPMGePoint3DArray& ptCircArr);
-	CPmSolid * CreateBall(const PMSoft::CPMGePoint3D& ptCent, double dRadius, PMSoft::PMBoolean3d::Ent3dData& drawData);
-	CPmSolid * CreateBall(const PMSoft::CPMGePoint3D& ptCent, double dRadius);
-	CPmSolid * CreateBall(const PMSoft::CPMGePoint3D& ptCent, double dRadius, double dHeight);
-	CPmSolid * CreateBall(const PMSoft::CPMGePoint3D& ptCent, double dRadius, double dHeight, PMSoft::PMBoolean3d::Ent3dData& drawData);
-	virtual CPmSolid * CreateBallBoard(const PMSoft::CPMGePoint3D& ptCent, double dHeight, double dRadius, double dBoardHeight);
-	virtual CPmSolid * createPipe(const PMSoft::CPMGePoint3D& axisStart, PMSoft::CPMGePoint3D& axisEnd, 
-		const PMSoft::CPMGeVector3D& baseNormal,
-		double dblOuterRadius, double dblInnerRadius);
-	virtual CPmSolid * createCone(const PMSoft::CPMGePoint3D& axisStart, const PMSoft::CPMGePoint3D& axisEnd, 
-		double radius1, double radius2);
-	virtual CPmSolid * createEllipsoid(const PMSoft::CPMGePoint3D &basept,double height,double radius1,double radius2,double radius3);
-	virtual CPmSolid * createPyramid(const PMSoft::CPMGePoint3DArray &Pt3d, const PMSoft::CPMGeVector3D &plgNormal, 
-		const PMSoft::CPMGePoint3D &apex);
-	virtual CPmSolid * createPyramid(const PMSoft::CPMGePoint3DArray &Pt3d, const PMSoft::CPMGeVector3D &plgNormal, 
-		const PMSoft::CPMGePoint3DArray &apexs);
 	virtual CPmSolid * createHelix(const PMSoft::CPMGePoint3DArray &pt3d, 
 		const PmGeDoubleArray bulges, 
 		const PMSoft::CPMGePoint3D &axis_start,