Implement compute_area function for triangles and use it in shape simpl.

Author: fontanf

include/packingsolver/irregular/shape.hpp

@@ -14,6 +14,10 @@ using ItemShapePos = int64_t;
 using ShapePos = int64_t;
 using Counter = int64_t;
 
+////////////////////////////////////////////////////////////////////////////////
+//////////////////////////////////// Point /////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
 /**
  * Structure for a point.
  */
@@ -89,6 +93,21 @@ Angle angle_radian(
         const Point& vector_1,
         const Point& vector_2);
 
+inline AreaDbl compute_area(
+        const Point& point_1,
+        const Point& point_2,
+        const Point& point_3)
+{
+    // https://en.wikipedia.org/wiki/Area_of_a_triangle#Using_coordinates
+    return 0.5 * (
+            (point_1.x - point_3.x) * (point_2.y - point_1.y)
+            - (point_1.x - point_2.x) * (point_3.y - point_1.y));
+}
+
+////////////////////////////////////////////////////////////////////////////////
+///////////////////////////////// ShapeElement /////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
 enum class ShapeElementType
 {
     LineSegment,

src/irregular/shape_simplification.cpp

@@ -204,11 +204,10 @@ AreaDbl compute_approximation_cost(
                     return std::numeric_limits<Angle>::infinity();
                 LengthDbl xp = ((x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) / denom;
                 LengthDbl yp = ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)) / denom;
-                AreaDbl cost = shape.copies * build_shape({
-                        {element.element.start.x}, {element.element.start.y},
+                AreaDbl cost = shape.copies * compute_area(
+                        element.element.start,
                         {xp, yp},
-                        {element.element.end.x, element.element.end.y}
-                        }).compute_area();
+                        element.element.end);
                 if (cost < 0)
                     return std::numeric_limits<Angle>::infinity();
                 return cost;
@@ -218,11 +217,10 @@ AreaDbl compute_approximation_cost(
             }
         } else {
             // angle_next < M_PI
-            Angle cost = shape.copies * build_shape({
-                    {element.element.start.x, element.element.start.y},
-                    {element_next.element.end.x, element_next.element.end.y},
-                    {element.element.end.x, element.element.end.y}
-                    }).compute_area();
+            Angle cost = shape.copies * compute_area(
+                    element.element.start,
+                    element_next.element.end,
+                    element.element.end);
             if (cost < 0) {
                 throw std::runtime_error(
                         "irregular::compute_approximation_cost: outer; "
@@ -260,10 +258,10 @@ AreaDbl compute_approximation_cost(
                     return std::numeric_limits<Angle>::infinity();
                 LengthDbl xp = ((x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) / denom;
                 LengthDbl yp = ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)) / denom;
-                AreaDbl cost = shape.copies * build_shape({
-                        {element.element.start.x, element.element.start.y},
-                        {element.element.end.x, element.element.end.y},
-                        {xp, yp}}).compute_area();
+                AreaDbl cost = shape.copies * compute_area(
+                        element.element.start,
+                        element.element.end,
+                        {xp, yp});
                 if (cost < 0)
                     return std::numeric_limits<Angle>::infinity();
                 return cost;
@@ -273,11 +271,10 @@ AreaDbl compute_approximation_cost(
             }
         } else {
             // angle_next < M_PI
-            Angle cost = shape.copies * build_shape({
-                    {element.element.start.x, element.element.start.y},
-                    {element.element.end.x, element.element.end.y},
-                    {element_next.element.end.x, element_next.element.end.y}
-                    }).compute_area();
+            Angle cost = shape.copies * compute_area(
+                    element.element.start,
+                    element.element.end,
+                    element_next.element.end);
             if (cost < 0) {
                 throw std::runtime_error(
                         "irregular::compute_approximation_cost: inner; "
@@ -384,10 +381,10 @@ void apply_approximation(
                 }
                 LengthDbl xp = ((x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) / denom;
                 LengthDbl yp = ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)) / denom;
-                AreaDbl cost = build_shape({
-                        {element.element.start.x, element.element.start.y},
-                        {element.element.end.x, element.element.end.y},
-                        {xp, yp}}).compute_area();
+                AreaDbl cost = compute_area(
+                        element.element.start,
+                        element.element.end,
+                        {xp, yp});
                 element_prev.element.end = {xp, yp};
                 element_next.element.start = {xp, yp};
             } else {