Merge pull request #4 from pFernbach/master

DeCasteljau and Curve splitting 

include/spline/bezier_curve.h

@@ -258,6 +258,82 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
 
     const t_point_t& waypoints() const {return pts_;}
 
+
+    /**
+     * @brief evalDeCasteljau evaluate the curve value at time t using deCasteljau algorithm
+     * @param t unNormalized time
+     * @return the point at time t
+     */
+    point_t evalDeCasteljau(const Numeric T) const {
+        // normalize time :
+        const Numeric t = T/T_;
+        t_point_t pts = deCasteljauReduction(waypoints(),t);
+        while(pts.size() > 1){
+            pts = deCasteljauReduction(pts,t);
+        }
+        return pts[0]*mult_T_;
+    }
+
+    t_point_t deCasteljauReduction(const Numeric t) const{
+        return deCasteljauReduction(waypoints(),t/T_);
+    }
+
+    /**
+     * @brief deCasteljauReduction compute the de Casteljau's reduction of the given list of points at time t
+     * @param pts the original list of points
+     * @param t the NORMALIZED time
+     * @return the reduced list of point (size of pts - 1)
+     */
+    t_point_t deCasteljauReduction(const t_point_t& pts, const Numeric t) const{
+        if(t < 0 || t > 1)
+            throw std::out_of_range("In deCasteljau reduction : t is not in [0;1]");
+        if(pts.size() == 1)
+            return pts;
+
+        t_point_t new_pts;
+        for(cit_point_t cit = pts.begin() ; cit != (pts.end() - 1) ; ++cit){
+            new_pts.push_back((1-t) * (*cit) + t*(*(cit+1)));
+        }
+        return new_pts;
+    }
+
+
+    /**
+     * @brief split split the curve in 2 at time t
+     * @param t
+     * @return
+     */
+    std::pair<bezier_curve_t,bezier_curve_t> split(const Numeric T){
+        t_point_t wps_first(size_),wps_second(size_);
+        const double t = T/T_;
+        wps_first[0] = pts_.front();
+        wps_second[degree_] = pts_.back();
+        t_point_t casteljau_pts = waypoints();
+        size_t id = 1;
+        while(casteljau_pts.size() > 1){
+            casteljau_pts = deCasteljauReduction(casteljau_pts,t);
+            wps_first[id] = casteljau_pts.front();
+            wps_second[degree_-id] = casteljau_pts.back();
+            ++id;
+        }
+
+        bezier_curve_t c_first(wps_first.begin(), wps_first.end(), T,mult_T_);
+        bezier_curve_t c_second(wps_second.begin(), wps_second.end(), T_-T,mult_T_);
+        return std::make_pair(c_first,c_second);
+    }
+
+    bezier_curve_t extract(const Numeric t1, const Numeric t2){
+        if(t1 < 0. || t1 > T_ || t2 < 0. || t2 > T_)
+            throw std::out_of_range("In Extract curve : times out of bounds");
+        if(t1 == 0.)
+            return split(t2).first;
+        if(t2 == T_)
+            return split(t1).second;
+
+        std::pair<bezier_curve_t,bezier_curve_t> c_split = this->split(t1);
+        return c_split.second->split(t2).first;
+    }
+
     private:
     template<typename In>
     t_point_t add_constraints(In PointsBegin, In PointsEnd, const curve_constraints_t& constraints)

src/tests/spline_test/Main.cpp

@@ -255,7 +255,7 @@ void BezierCurveTestCompareHornerAndBernstein(bool& /*error*/)
     // 3d curve
     bezier_curve_t cf(params.begin(), params.end());
 
-    clock_t s0,e0,s1,e1,s2,e2;
+    clock_t s0,e0,s1,e1,s2,e2,s3,e3;
     s0 = clock();
     for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
     {
@@ -277,12 +277,18 @@ void BezierCurveTestCompareHornerAndBernstein(bool& /*error*/)
     }
     e2 = clock();
 
-
-    std::cout << "time for analytical eval " <<   double(e0 - s0) / CLOCKS_PER_SEC << std::endl;
-    std::cout << "time for bernstein eval "  <<   double(e1 - s1) / CLOCKS_PER_SEC << std::endl;
-    std::cout << "time for horner eval "     <<   double(e2 - s2) / CLOCKS_PER_SEC << std::endl;
+    s3 = clock();
+    for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
+    {
+        cf.evalDeCasteljau(*cit);
+    }
+    e3 = clock();
 
 
+    std::cout << "time for analytical eval  " <<   double(e0 - s0) / CLOCKS_PER_SEC << std::endl;
+    std::cout << "time for bernstein eval   "  <<   double(e1 - s1) / CLOCKS_PER_SEC << std::endl;
+    std::cout << "time for horner eval      "     <<   double(e2 - s2) / CLOCKS_PER_SEC << std::endl;
+    std::cout << "time for deCasteljau eval "     <<   double(e3 - s3) / CLOCKS_PER_SEC << std::endl;
 
     std::cout << "now with high order polynom "    << std::endl;
 
@@ -317,10 +323,19 @@ void BezierCurveTestCompareHornerAndBernstein(bool& /*error*/)
     }
     e0 = clock();
 
+    s3 = clock();
+    for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
+    {
+        cf2.evalDeCasteljau(*cit);
+    }
+    e3 = clock();
+
+
 
-    std::cout << "time for analytical eval " <<   double(e0 - s0) / CLOCKS_PER_SEC << std::endl;
-    std::cout << "time for bernstein eval "  <<   double(e1 - s1) / CLOCKS_PER_SEC << std::endl;
-    std::cout << "time for horner eval "     <<   double(e2 - s2) / CLOCKS_PER_SEC << std::endl;
+    std::cout << "time for analytical eval  " <<   double(e0 - s0) / CLOCKS_PER_SEC << std::endl;
+    std::cout << "time for bernstein eval   "  <<   double(e1 - s1) / CLOCKS_PER_SEC << std::endl;
+    std::cout << "time for horner eval      "     <<   double(e2 - s2) / CLOCKS_PER_SEC << std::endl;
+    std::cout << "time for deCasteljau eval "     <<   double(e3 - s3) / CLOCKS_PER_SEC << std::endl;
 
 }
 
@@ -768,6 +783,143 @@ void TestReparametrization(bool& error)
     }
 }
 
+point_t randomPoint(const double min, const double max ){
+    point_t p;
+    for(size_t i = 0 ; i < 3 ; ++i)
+        p[i] =  (rand()/(double)RAND_MAX ) * (max-min) + min;
+    return p;
+}
+
+void BezierEvalDeCasteljau(bool& error){
+    using namespace std;
+    std::vector<double> values;
+    for (int i =0; i < 100000; ++i)
+        values.push_back(rand()/RAND_MAX);
+
+    //first compare regular evaluation (low dim pol)
+    point_t a(1,2,3);
+    point_t b(2,3,4);
+    point_t c(3,4,5);
+    point_t d(3,6,7);
+    point_t e(3,61,7);
+    point_t f(3,56,7);
+    point_t g(3,36,7);
+    point_t h(43,6,7);
+    point_t i(3,6,77);
+
+    std::vector<point_t> params;
+    params.push_back(a);
+    params.push_back(b);
+    params.push_back(c);
+
+    // 3d curve
+    bezier_curve_t cf(params.begin(), params.end());
+
+    for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
+    {
+        if(cf.evalDeCasteljau(*cit) != cf(*cit)){
+            error = true;
+            std::cout<<" De Casteljau evaluation did not return the same value as analytical"<<std::endl;
+        }
+    }
+
+    params.push_back(d);
+    params.push_back(e);
+    params.push_back(f);
+    params.push_back(g);
+    params.push_back(h);
+    params.push_back(i);
+
+    bezier_curve_t cf2(params.begin(), params.end());
+
+    for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
+    {
+        if(cf.evalDeCasteljau(*cit) != cf(*cit)){
+            error = true;
+            std::cout<<" De Casteljau evaluation did not return the same value as analytical"<<std::endl;
+        }
+    }
+
+}
+
+
+/**
+ * @brief BezierSplitCurve test the 'split' method of bezier curve
+ * @param error
+ */
+void BezierSplitCurve(bool& error){
+    // test for degree 5
+    int n = 5;
+    double t_min = 0.2;
+    double t_max = 10;
+    for(size_t i = 0 ; i < 1 ; ++i){
+        // build a random curve and split it at random time :
+        //std::cout<<"build a random curve"<<std::endl;
+        point_t a;
+        std::vector<point_t> wps;
+        for(size_t j = 0 ; j <= n ; ++j){
+            wps.push_back(randomPoint(-10.,10.));
+        }
+        double t = (rand()/(double)RAND_MAX )*(t_max-t_min) + t_min;
+        double ts = (rand()/(double)RAND_MAX )*(t);
+
+        bezier_curve_t c(wps.begin(), wps.end(),t);
+        std::pair<bezier_curve_t,bezier_curve_t> cs = c.split(ts);
+        //std::cout<<"split curve of duration "<<t<<" at "<<ts<<std::endl;
+
+        // test on splitted curves :
+
+        if(! ((c.degree_ == cs.first.degree_) && (c.degree_ == cs.second.degree_) )){
+            error = true;
+            std::cout<<" Degree of the splitted curve are not the same as the original curve"<<std::endl;
+        }
+
+        if(c.max() != (cs.first.max() + cs.second.max())){
+            error = true;
+            std::cout<<"Duration of the splitted curve doesn't correspond to the original"<<std::endl;
+        }
+
+        if(c(0) != cs.first(0)){
+            error = true;
+            std::cout<<"initial point of the splitted curve doesn't correspond to the original"<<std::endl;
+        }
+
+        if(c(t) != cs.second(cs.second.max())){
+            error = true;
+            std::cout<<"final point of the splitted curve doesn't correspond to the original"<<std::endl;
+        }
+
+        if(cs.first.max() != ts){
+            error = true;
+            std::cout<<"timing of the splitted curve doesn't correspond to the original"<<std::endl;
+        }
+
+        if(cs.first(ts) != cs.second(0.)){
+            error = true;
+            std::cout<<"splitting point of the splitted curve doesn't correspond to the original"<<std::endl;
+        }
+
+        // check along curve :
+        double ti = 0.;
+        while(ti <= ts){
+            if((cs.first(ti) - c(ti)).norm() > 1e-14){
+                error = true;
+                std::cout<<"first splitted curve and original curve doesn't correspond, error = "<<cs.first(ti) - c(ti) <<std::endl;
+            }
+            ti += 0.01;
+        }
+        while(ti <= t){
+            if((cs.second(ti-ts) - c(ti)).norm() > 1e-14){
+                error = true;
+                std::cout<<"second splitted curve and original curve doesn't correspond, error = "<<cs.second(ti-ts) - c(ti)<<std::endl;
+            }
+            ti += 0.01;
+        }
+    }
+}
+
+
+
 int main(int /*argc*/, char** /*argv[]*/)
 {
     std::cout << "performing tests... \n";
@@ -789,7 +941,9 @@ int main(int /*argc*/, char** /*argv[]*/)
     BezierCurveTestCompareHornerAndBernstein(error);
     BezierDerivativeCurveTimeReparametrizationTest(error);
     BezierToPolynomConversionTest(error);
-	if(error)
+    BezierEvalDeCasteljau(error);
+    BezierSplitCurve(error);
+    if(error)
 	{
         std::cout << "There were some errors\n";
 		return -1;