geom/tri: add tri sampler

geom/tri.hpp

@@ -17,23 +17,63 @@
 #ifndef CRUFT_GEOM_TRI_HPP
 #define CRUFT_GEOM_TRI_HPP
 
-#include <cstddef>
-
 #include "../point.hpp"
+#include "sample.hpp"
+
+#include <cstddef>
+#include <random>
 
 namespace util::geom {
+    ///////////////////////////////////////////////////////////////////////////
+    template <size_t S, typename T>
+    struct tri {
+        tri () = default;
+        tri (point<S,T> _a, point<S,T> _b, point<S,T> _c):
+            a (_a), b (_b), c (_c)
+        { ; }
+
+        util::point<S,T> a, b, c;
+    };
+
+    template <size_t S, typename T>
+    tri (point<S,T>, point<S,T>, point<S,T>) -> tri<S,T>;
+
+    using tri3f = tri<3,float>;
+
+
+    namespace surface {
+        template <size_t S, typename T>
+        struct sampler<tri<S,T>> {
+            sampler (tri<S,T> _target):
+                base (_target.a),
+                v0 (_target.b - _target.a),
+                v1 (_target.c - _target.a)
+            { ; }
+
+            template <typename GeneratorT>
+            util::point<S,T>
+            operator() (GeneratorT &&gen) const noexcept
+            {
+                std::uniform_real_distribution<float> dist (0, 1);
+                return base + dist (gen) * v0 + dist (gen) * v1;
+            }
+
+            util::point<S,T> base;
+            util::vector<S,T> v0, v1;
+        };
+    };
+
+
     ///////////////////////////////////////////////////////////////////////////
     // n-dimensional triangle area
     template <std::size_t DimensionV, typename ValueT>
     ValueT
-    area (util::point<DimensionV,ValueT> a,
+    area (tri<DimensionV,ValueT> obj)
-          util::point<DimensionV,ValueT> b,
-          util::point<DimensionV,ValueT> c)
     {
         // heron's formula
-        const auto ab = util::distance (a, b);
+        const auto ab = util::distance (obj.a, obj.b);
-        const auto bc = util::distance (b, c);
+        const auto bc = util::distance (obj.b, obj.c);
-        const auto ca = util::distance (c, a);
+        const auto ca = util::distance (obj.c, obj.a);
 
         const auto s = (ab + bc + ca) / 2;
 
@@ -45,19 +85,19 @@ namespace util::geom {
     // 2-dimension triangle area
     template <typename T>
     T
-    area (util::point<2,T> a, util::point<2,T> b, util::point<2,T> c)
+    area (tri<2,T> obj)
     {
         //                | x1 y1 1 |
         // area = 0.5 det | x2 y2 1 |
         //                | x3 y3 1 |
 
         return std::abs (
-            -b.x * a.y
+            -obj.b.x * obj.a.y
-            +c.x * a.y
+            +obj.c.x * obj.a.y
-            +a.x * b.y
+            +obj.a.x * obj.b.y
-            -c.x * b.y
+            -obj.c.x * obj.b.y
-            -a.x * c.y
+            -obj.a.x * obj.c.y
-            +b.x * c.y
+            +obj.b.x * obj.c.y
         ) / 2;
     }
 
@@ -66,13 +106,23 @@ namespace util::geom {
     // 3-dimension triangle area
     template <typename T>
     T
-    area (util::point<3,T> a, util::point<3,T> b, util::point<3,T> c)
+    area (tri<3,T> obj)
     {
-        const auto ab = a - b;
+        const auto ab = obj.a - obj.b;
-        const auto ac = a - c;
+        const auto ac = obj.a - obj.c;
 
         return norm (cross (ab, ac)) / 2;
     }
+
+
+    //-------------------------------------------------------------------------
+    // convenience forwarder
+    template <size_t S, typename T>
+    T
+    area (point<S,T> a, point<S,T> b, point<S,T> c)
+    {
+        return area (tri (a, b, c));
+    }
 };
 
 #endif