add Polygon sdf (PaddlePaddle#406)

* add Polygon sdf

* add Polygon sdf

* rewrite Polygon sdf

* rewrite Polygon sdf

* rewrite Polygon sdf

* rewrite Polygon sdf

* rewrite Polygon sdf

* rewrite Polygon sdf

* rewrite Polygon sdf and add some annotations

* rewrite Polygon sdf

* rewrite Polygon sdf

* rewrite Polygon sdf

* rewrite Polygon sdf

ppsci/geometry/geometry_2d.py

@@ -599,6 +599,51 @@ def random_boundary_points(self, n, random="pseudo"):
             x.append((l - l0) * v + self.vertices[i])
         return np.vstack(x)
 
+    def sdf_func(self, points: np.ndarray) -> np.ndarray:
+        """Compute signed distance field.
+        Args:
+            points (np.ndarray): The coordinate points used to calculate the SDF value,
+                the shape is [N, 2]
+        Returns:
+            np.ndarray: Unsquared SDF values of input points, the shape is [N, 1].
+        NOTE: This function usually returns ndarray with negative values, because
+        according to the definition of SDF, the SDF value of the coordinate point inside
+        the object(interior points) is negative, the outside is positive, and the edge
+        is 0. Therefore, when used for weighting, a negative sign is often added before
+        the result of this function.
+        """
+        sdf_value = np.empty((points.shape[0], 1), dtype=paddle.get_default_dtype())
+        for n in range(points.shape[0]):
+            distance = np.dot(
+                points[n] - self.vertices[0], points[n] - self.vertices[0]
+            )
+            inside_tag = 1.0
+            for i in range(self.vertices.shape[0]):
+                j = (self.vertices.shape[0] - 1) if i == 0 else (i - 1)
+                # Calculate the shortest distance from point P to each edge.
+                vector_ij = self.vertices[j] - self.vertices[i]
+                vector_in = points[n] - self.vertices[i]
+                distance_vector = vector_in - vector_ij * np.clip(
+                    np.dot(vector_in, vector_ij) / np.dot(vector_ij, vector_ij),
+                    0.0,
+                    1.0,
+                )
+                distance = np.minimum(
+                    distance, np.dot(distance_vector, distance_vector)
+                )
+                # Calculate the inside and outside using the Odd-even rule
+                odd_even_rule_number = np.array(
+                    [
+                        points[n][1] >= self.vertices[i][1],
+                        points[n][1] < self.vertices[j][1],
+                        vector_ij[0] * vector_in[1] > vector_ij[1] * vector_in[0],
+                    ]
+                )
+                if odd_even_rule_number.all() or np.all(~odd_even_rule_number):
+                    inside_tag *= -1.0
+            sdf_value[n] = inside_tag * np.sqrt(distance)
+        return -sdf_value
+
 
 def polygon_signed_area(vertices):
     """The (signed) area of a simple polygon.