Add a command to show center of mass, assuming uniform density.

CHANGELOG.md

@@ -39,15 +39,19 @@ New rendering features:
     or not drawing them at all.
   * The "Show/hide outlines" button is now independent from "Show/hide edges".
 
-Other new features:
-  * New command-line interface, for batch exporting and more.
+New measurement/analysis features:
   * New command for measuring total length of selected entities,
     "Analyze → Measure Perimeter".
+  * New command for measuring center of mass, with live updates as the sketch
+    changes, "Analyze → Center of Mass".
+  * When selecting a point and a line, projected distance to to current
+    workplane is displayed.
+
+Other new features:
+  * New command-line interface, for batch exporting and more.
   * New link to match the on-screen size of the sketch with its actual size,
     "view → set to full scale".
   * When zooming to fit, constraints are also considered.
-  * When selecting a point and a line, projected distance to to current
-    workplane is displayed.
   * When clicking on an entity that shares a place with other entities,
     the entity from the current group is selected.
   * When dragging an entity that shares a place with other entities,

src/draw.cpp

@@ -770,6 +770,33 @@ void GraphicsWindow::Draw(Canvas *canvas) {
         canvas->DrawLine(SS.extraLine.ptA, SS.extraLine.ptB, hcsDatum);
     }
 
+    if(SS.centerOfMass.draw && !SS.centerOfMass.dirty) {
+        Vector p = SS.centerOfMass.position;
+        Vector u = camera.projRight;
+        Vector v = camera.projUp;
+
+        const double size = 10.0;
+        const int subdiv = 16;
+        double h = Style::DefaultTextHeight() / camera.scale;
+        canvas->DrawVectorText(ssprintf("%.3f, %.3f, %.3f", p.x, p.y, p.z), h,
+                               p.Plus(u.ScaledBy((size + 5.0)/scale)).Minus(v.ScaledBy(h / 2.0)),
+                               u, v,hcsDatum);
+        u = u.WithMagnitude(size / scale);
+        v = v.WithMagnitude(size / scale);
+
+        canvas->DrawLine(p.Minus(u), p.Plus(u), hcsDatum);
+        canvas->DrawLine(p.Minus(v), p.Plus(v), hcsDatum);
+        Vector prev;
+        for(int i = 0; i <= subdiv; i++) {
+            double a = (double)i / subdiv * 2.0 * PI;
+            Vector point = p.Plus(u.ScaledBy(cos(a))).Plus(v.ScaledBy(sin(a)));
+            if(i > 0) {
+                canvas->DrawLine(point, prev, hcsDatum);
+            }
+            prev = point;
+        }
+    }
+
     // A note to indicate the origin in the just-exported file.
     if(SS.justExportedInfo.draw) {
         Vector p, u, v;

src/generate.cpp

@@ -359,6 +359,7 @@ void SolveSpaceUI::GenerateAll(Generate type, bool andFindFree, bool genForBBox)
     FreeAllTemporary();
     allConsistent = true;
     SS.GW.persistentDirty = true;
+    SS.centerOfMass.dirty = true;
 
     endMillis = GetMilliseconds();
 
@@ -418,6 +419,12 @@ void SolveSpaceUI::ForceReferences() {
     }
 }
 
+void SolveSpaceUI::UpdateCenterOfMass() {
+    SMesh *m = &(SK.GetGroup(SS.GW.activeGroup)->displayMesh);
+    SS.centerOfMass.position = m->GetCenterOfMass();
+    SS.centerOfMass.dirty = false;
+}
+
 void SolveSpaceUI::MarkDraggedParams() {
     sys.dragged.Clear();
 

src/graphicswin.cpp

@@ -152,6 +152,7 @@ const GraphicsWindow::MenuEntry GraphicsWindow::menu[] = {
 { 1, N_("Measure &Perimeter"),          Command::PERIMETER,        C|S|'P', TN, mAna  },
 { 1, N_("Show &Interfering Parts"),     Command::INTERFERENCE,     C|S|'I', TN, mAna  },
 { 1, N_("Show &Naked Edges"),           Command::NAKED_EDGES,      C|S|'N', TN, mAna  },
+{ 1, N_("Show &Center of Mass"),        Command::CENTER_OF_MASS,      C|S|'C', TN, mAna  },
 { 1, NULL,                              Command::NONE,             0,       TN, NULL  },
 { 1, N_("Show Degrees of &Freedom"),    Command::SHOW_DOF,         C|S|'F', TN, mAna  },
 { 1, NULL,                              Command::NONE,             0,       TN, NULL  },
@@ -793,6 +794,7 @@ void GraphicsWindow::MenuEdit(Command id) {
             SS.TW.HideEditControl();
             SS.nakedEdges.Clear();
             SS.justExportedInfo.draw = false;
+            SS.centerOfMass.draw = false;
             // This clears the marks drawn to indicate which points are
             // still free to drag.
             Param *p;

src/groupmesh.cpp

@@ -421,6 +421,10 @@ void Group::GenerateDisplayItems() {
         // work correctly.
         displayMesh.PrecomputeTransparency();
 
+        // Recalculate mass center if needed
+        if(SS.centerOfMass.draw && SS.centerOfMass.dirty && h.v == SS.GW.activeGroup.v) {
+            SS.UpdateCenterOfMass();
+        }
         displayDirty = false;
     }
 }

src/mesh.cpp

@@ -345,6 +345,18 @@ uint32_t SMesh::FirstIntersectionWith(Point2d mp) const {
     return face;
 }
 
+Vector SMesh::GetCenterOfMass() const {
+    Vector center = {};
+    double vol = 0.0;
+    for(int i = 0; i < l.n; i++) {
+        STriangle &tr = l.elem[i];
+        double tvol = tr.SignedVolume();
+        center = center.Plus(tr.a.Plus(tr.b.Plus(tr.c)).ScaledBy(tvol / 4.0));
+        vol += tvol;
+    }
+    return center.ScaledBy(1.0 / vol);
+}
+
 STriangleLl *STriangleLl::Alloc()
     { return (STriangleLl *)AllocTemporary(sizeof(STriangleLl)); }
 SKdNode *SKdNode::Alloc()

src/polygon.cpp

@@ -83,6 +83,10 @@ bool STriangle::Raytrace(const Vector &rayPoint, const Vector &rayDir,
     return true;
 }
 
+double STriangle::SignedVolume() const {
+    return a.Dot(b.Cross(c)) / 6.0;
+}
+
 void STriangle::FlipNormal() {
     swap(a, b);
     swap(an, bn);

src/polygon.h

@@ -190,6 +190,7 @@ public:
     STriangle Transform(Vector o, Vector u, Vector v) const;
     bool Raytrace(const Vector &rayPoint, const Vector &rayDir,
                   double *t, Vector *inters) const;
+    double SignedVolume() const;
 };
 
 class SBsp2 {
@@ -282,6 +283,8 @@ public:
     void RemapFaces(Group *g, int remap);
 
     uint32_t FirstIntersectionWith(Point2d mp) const;
+
+    Vector GetCenterOfMass() const;
 };
 
 // A linked list of triangles

src/solvespace.cpp

@@ -311,6 +311,7 @@ void SolveSpaceUI::AfterNewFile() {
 
     // Quit export mode
     justExportedInfo.draw = false;
+    centerOfMass.draw = false;
     exportMode = false;
 
     // GenerateAll() expects the view to be valid, because it uses that to
@@ -616,6 +617,13 @@ void SolveSpaceUI::MenuAnalyze(Command id) {
             break;
         }
 
+        case Command::CENTER_OF_MASS: {
+            SS.UpdateCenterOfMass();
+            SS.centerOfMass.draw = true;
+            InvalidateGraphics();
+            break;
+        }
+
         case Command::VOLUME: {
             SMesh *m = &(SK.GetGroup(SS.GW.activeGroup)->displayMesh);
 

src/solvespace.h

@@ -810,6 +810,11 @@ public:
         bool        draw, showOrigin;
         Vector      pt, u, v;
     } justExportedInfo;
+    struct {
+        bool   draw;
+        bool   dirty;
+        Vector position;
+    } centerOfMass;
 
     class Clipboard {
     public:
@@ -857,6 +862,7 @@ public:
     void WriteEqSystemForGroup(hGroup hg);
     void MarkDraggedParams();
     void ForceReferences();
+    void UpdateCenterOfMass();
 
     bool ActiveGroupsOkay();
 

src/ui.h

@@ -213,6 +213,7 @@ enum class Command : uint32_t {
     INTERFERENCE,
     NAKED_EDGES,
     SHOW_DOF,
+    CENTER_OF_MASS,
     TRACE_PT,
     STOP_TRACING,
     STEP_DIM,