[pyramid_com] computation of center of mass of pyramids with less divisions ()

Merging branch 'pyramid_com'  into 'main'.

See merge request !1160

Sample/HardParticle/Pyramid2.cpp

@@ -64,8 +64,8 @@ std::string Pyramid2::validate() const
     double W = m_width / 2;
     double w = m_width / 2 * (1 - s);
 
-    double zcom =
-        m_height * (.5 - (r + s) / 3 + r * s / 4) / (1 - (r + s) / 2 + r * s / 3); // center of mass
+    // center of mass
+    double zcom = m_height * 0.5 * (6 - 4 * (r + s) + 3 * r * s) / (6 - 3 * (r + s) + 2 * r * s);
 
     setPolyhedron(topology, -zcom,
                   {// base:

Sample/HardParticle/Pyramid3.cpp

@@ -55,14 +55,15 @@ std::string Pyramid3::validate() const
 
     double a = m_base_edge;
     double as = a / 2;
-    double ac = a / sqrt(3) / 2;
-    double ah = a / sqrt(3);
+    double ac = a * (1. / sqrt(3) / 2);
+    double ah = a * (1. / sqrt(3));
     double b = a * (1 - r);
     double bs = b / 2;
-    double bc = b / sqrt(3) / 2;
-    double bh = b / sqrt(3);
+    double bc = b * (1. / sqrt(3) / 2);
+    double bh = b * (1. / sqrt(3));
 
-    double zcom = m_height * (.5 - 2 * r / 3 + r * r / 4) / (1 - r + r * r / 3); // center of mass
+    // center of mass
+    double zcom = m_height * (1. / 4) * (6 - 8 * r + 3 * r * r) / (3 - 3 * r + r * r);
 
     setPolyhedron(topology, -zcom,
                   {// base:

Sample/HardParticle/Pyramid4.cpp

@@ -58,7 +58,8 @@ std::string Pyramid4::validate() const
     double a = m_base_edge / 2;
     double b = a * (1 - r);
 
-    double zcom = m_height * (.5 - 2 * r / 3 + r * r / 4) / (1 - r + r * r / 3); // center of mass
+    // center of mass
+    double zcom = m_height * (1. / 4) * (6 - 8 * r + 3 * r * r) / (3 - 3 * r + r * r);
 
     setPolyhedron(topology, -zcom,
                   {// base: