refactor line geometry def; solve circle & eval for polylines with bugles

include/line.hpp

@@ -3,28 +3,32 @@
 #include <vector>
 #include <iostream>
 #include <memory>
+#include <cassert>
+#include <cmath>
+
+// class ILineParam {
+// public:
+//     virtual ~ILineParam() = default;
+// };
+//
+// class PolylineParam : ILineParam {
+//     int segIdx;
+//     real tOnSeg;
+// };
+//
+// class PolynomialLineParam : ILineParam {
+//     real t;
+// };
 
-class ILineParam {
+class ILine {
 public:
-    virtual ~ILineParam() = default;
-};
-
-struct PolylineParam : ILineParam {
-    int segIdx;
-    real tOnSeg;
-};
+    virtual ~ILine() = default;
 
-struct PolynomialLineParam : ILineParam {
-    real t;
-};
+    virtual Vec3 eval(const double param) const = 0;
 
-class ILine {
-    public:
-    virtual ~ILine() = default;
+    virtual Vec3 tangent(const double param) const = 0;
 
-    virtual Vec3 eval(const ILineParam& param) const = 0;
-    virtual Vec3 tangent(const ILineParam& param) const = 0;
-    virtual std::unique_ptr<ILineParam> getClosestParam(const Vec3& p) const = 0;
+    virtual double getClosestParam(const Vec3 &p) const = 0;
 };
 
 template<size_t N>
@@ -32,42 +36,69 @@ using PtArray = std::vector<Vec<N> >;
 using Pt3Array = PtArray<3>;
 using Pt2Array = PtArray<2>;
 
-template<size_t N>
-class Polyline: public ILine {
+
+class Polyline : public ILine {
 public:
-    Polyline(const PtArray<N> &points, const std::vector<double> &bugles, bool closed = false) : points(points),
-        bugles(bugles), closed(closed) {
+    using Point = Vec<3>;
+
+    Polyline(const Pt3Array &points, const std::vector<double> &bugles, const Vec3 &normal, bool closed = false)
+        : points(points), bugles(bugles), closed(closed), normal(normal.normalize()) {
         assert(points.size() >= 2);
         if (closed) {
             assert(points.size() == bugles.size());
         } else {
-            assert(points.size() - 1 == bugles.size() || points.size() == bugles.size());
+            assert(points.size() - 1 == bugles.size());
+        }
+        circleCenters.resize(bugles.size());
+        thetas.resize(bugles.size());
+        radii.resize(bugles.size());
+        for (size_t i = 0; i < bugles.size(); ++i) {
+            const Point &A = points[i];
+            const Point &B = points[(i + 1) % points.size()];
+            Vec3 AB = B - A;
+            Vec3 ABNorm = AB.normalize();
+            Vec3 QO = normal.cross(ABNorm) * (abs(bugles[i]) > 1 ? -1 : 1);
+            float theta = std::atan(bugles[i]) * 4;
+            float h = AB.length() * 0.5 * std::tan(theta * 0.5);
+            circleCenters[i] = A + AB * 0.5 + QO * h;
+            thetas[i] = theta;
+            radii[i] = (circleCenters[i] - A).length();
         }
     }
 
-    using Point = Vec<N>;
-
 private:
-    PtArray<N> points;
-    std::vector<double> bugles;
+    Pt3Array points;
+    std::vector<real> bugles;
+    Vec3 normal;
     bool closed;
 
+    Pt3Array circleCenters;
+    std::vector<real> thetas;
+    std::vector<real> radii;
+
 public:
+    Vec3 eval(const real param) const override {
+        assert(param >= 0 && param <= bugles.size());
+        int seg = static_cast<int>(param);
+        real tOnSeg = param - seg;
 
-    Vec3 eval(const ILineParam& param) const override {
-        const PolylineParam* polyParam = dynamic_cast<const PolylineParam*>(&param); // 进行类型检查
-        if (!polyParam) {
-            throw std::invalid_argument("Invalid parameter type for Polyline::eval");
-        }
-       // TODO:
+        const auto &A = points[seg];
+        // const auto &B = points[(seg + 1) % points.size()];
+        const auto &center = circleCenters[seg];
+        Vec3 u = (A-center).normalize();
+        Vec3 v = normal.cross(u);
+
+        real phi = tOnSeg * thetas[seg];
+        const auto &r = radii[seg];
+
+        return center + r * (u * std::cos(phi) + v * std::sin(phi));
     }
 
-    Vec3 tangent(const ILineParam& param) const override {
+    Vec3 tangent(const double param) const override {
         // TODO:
     }
 
-    std::unique_ptr<ILineParam> getClosestParam(const Vec3& p) const override {
-        auto closestParam = std::make_unique<PolylineParam>();
+    double getClosestParam(const Vec3 &p) const override {
         // TODO:
         return closestParam;
     }
@@ -76,8 +107,6 @@ public:
         points.push_back(point);
     }
 
-
-
     const Point &getPoint(size_t index) const {
         return points[index];
     }
@@ -103,6 +132,6 @@ public:
     }
 };
 
-class PolynomialLine: public ILine {
+class PolynomialLine : public ILine {
 public:
-};
+};

include/vec.hpp

@@ -2,11 +2,11 @@
 #include "real.hpp"
 #include <cmath>
 #include <array>
+#include <assert.h>
 
-template <size_t N>
+template<size_t N>
 class Vec {
 public:
-    using real = float; // 根据需要定义 real 类型
     std::array<real, N> data;
 
     Vec() {
@@ -17,24 +17,26 @@ public:
         std::copy(values.begin(), values.end(), data.begin());
     }
 
-    Vec(const Vec<N>& v) {
+    Vec(real... args) : data{static_cast<real>(args)...} {}
+
+    Vec(const Vec<N> &v) {
         data = v.data;
     }
 
-    Vec<N>& operator=(const Vec<N>& v) {
+    Vec<N> &operator=(const Vec<N> &v) {
         data = v.data;
         return *this;
     }
 
-    real& operator[](size_t index) {
+    real &operator[](size_t index) {
         return data[index];
     }
 
-    const real& operator[](size_t index) const {
+    const real &operator[](size_t index) const {
         return data[index];
     }
 
-    Vec<N> operator+(const Vec<N>& v) const {
+    Vec<N> operator+(const Vec<N> &v) const {
         Vec<N> result;
         for (size_t i = 0; i < N; ++i) {
             result[i] = data[i] + v[i];
@@ -42,7 +44,7 @@ public:
         return result;
     }
 
-    Vec<N> operator-(const Vec<N>& v) const {
+    Vec<N> operator-(const Vec<N> &v) const {
         Vec<N> result;
         for (size_t i = 0; i < N; ++i) {
             result[i] = data[i] - v[i];
@@ -58,6 +60,15 @@ public:
         return result;
     }
 
+    friend Vec<N> operator*(real s, const Vec<N> &v) {
+        Vec<N> result;
+        for (size_t i = 0; i < N; ++i) {
+            result[i] = s * v[i];
+        }
+        return result;
+    }
+
+
     Vec<N> operator/(real s) const {
         Vec<N> result;
         for (size_t i = 0; i < N; ++i) {
@@ -66,7 +77,7 @@ public:
         return result;
     }
 
-    real dot(const Vec<N>& v) const {
+    real dot(const Vec<N> &v) const {
         real sum = 0;
         for (size_t i = 0; i < N; ++i) {
             sum += data[i] * v[i];
@@ -82,12 +93,88 @@ public:
         return *this / norm();
     }
 
-    Vec<N> reflect(const Vec<N>& n) const {
+    Vec<N> reflect(const Vec<N> &n) const {
         return *this - n * 2 * dot(n);
     }
 };
 
-template <size_t N>
+
+// specialize template class Vec<3>;
+template<>
+class Vec<3> {
+public:
+    union {
+        std::array<real, 3> data;
+
+        struct {
+            real x, y, z;
+        };
+
+        struct {
+            real u, v, w;
+        };
+    };
+
+    Vec() : data{0, 0, 0} {}
+
+    Vec(real x, real y, real z) : data{x, y, z} {}
+
+    Vec(const Vec &v) : data{v.data[0], v.data[1], v.data[2]} {}
+
+    Vec &operator=(const Vec &v) {
+        data[0] = v.data[0];
+        data[1] = v.data[1];
+        data[2] = v.data[2];
+        return *this;
+    }
+
+    real operator[](size_t index) const {
+        return data[index];
+    }
+
+    real &operator[](size_t index) {
+        return data[index];
+    }
+
+    Vec operator+(const Vec &v) const {
+        return {x + v.x, y + v.y, z + v.z};
+    }
+
+    Vec operator-(const Vec &v) const {
+        return {x - v.x, y - v.y, z - v.z};
+    }
+
+    Vec operator*(real s) const {
+        return {x * s, y * s, z * s};
+    }
+
+    friend Vec operator*(real s, const Vec &v) {
+        return {s * v.x, s * v.y, s * v.z};
+    }
+
+
+    Vec operator/(real s) const {
+        assert(s != 0);
+        real inv = 1 / s;
+        return *this * inv;
+    }
+
+    real dot(const Vec &v) const {
+        return x * v.x + y * v.y + z * v.z;
+    }
+
+    real length() const {
+        return std::sqrt(dot(*this));
+    }
+
+    Vec normalize() const {
+            return *this / length();
+    }
+
+    Vec cross(const Vec &v) const {
+        return {y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x};
+    }
+};
 
 using Vec2 = Vec<2>;
 using Vec3 = Vec<3>;
@@ -141,4 +228,4 @@ using Vec3 = Vec<3>;
 //    Vec3 reflect(const Vec3& n) const {
 //        return *this - n * 2 * dot(n);
 //    }
-//};
+//};