Resolve "(LearnerND) add iso-surface plot feature"

Closes #112 (closed)

adaptive/learner/learnerND.py

@@ -10,7 +10,7 @@ import scipy.spatial
 
 from .base_learner import BaseLearner
 
-from ..notebook_integration import ensure_holoviews
+from ..notebook_integration import ensure_holoviews, ensure_plotly
 from .triangulation import (Triangulation, point_in_simplex,
                             circumsphere, simplex_volume_in_embedding)
 from ..utils import restore, cache_latest
@@ -576,3 +576,129 @@ class LearnerND(BaseLearner):
             return im.opts(style=dict(cmap='viridis'))
         else:
             raise ValueError("Only 1 or 2-dimensional plots can be generated.")
+
+    def _get_isosurface(self, level=0.0):
+        if self.ndim != 3 or self.vdim != 1:
+            raise Exception('Isosurface plotting is only supported'
+                            ' for a 3D input and 1D output')
+
+        vertices = []  # index -> (x,y,z)
+        faces = []  # tuple of indices of the corner points
+        from_line_to_vertex = {}  # the interpolated vertex (index) between two known points
+
+        def _get_vertex_index(a, b):
+            if (a, b) in from_line_to_vertex:
+                return from_line_to_vertex[(a, b)]
+
+            # Otherwise compute it and cache the result.
+            vertex_a = self.tri.vertices[a]
+            vertex_b = self.tri.vertices[b]
+            value_a = self.data[vertex_a]
+            value_b = self.data[vertex_b]
+
+            da = abs(value_a - level)
+            db = abs(value_b - level)
+            dab = da + db
+
+            new_pt = (db / dab * np.array(vertex_a)
+                      + da / dab * np.array(vertex_b))
+
+            new_index = len(vertices)
+            vertices.append(new_pt)
+            from_line_to_vertex[(a, b)] = new_index
+            return new_index
+
+        for simplex in self.tri.simplices:
+            plane = []
+            for a, b in itertools.combinations(simplex, 2):
+                va = self.data[self.tri.vertices[a]]
+                vb = self.data[self.tri.vertices[b]]
+                if min(va, vb) < level <= max(va, vb):
+                    vi = _get_vertex_index(a, b)
+                    should_add = True
+                    for pi in plane:
+                        if np.allclose(vertices[vi], vertices[pi]):
+                            should_add = False
+                    if should_add:
+                        plane.append(vi)
+
+            if len(plane) == 3:
+                faces.append(plane)
+            elif len(plane) == 4:
+                faces.append(plane[:3])
+                faces.append(plane[1:])
+
+        if len(faces) == 0:
+            r_min = min(self.data[v] for v in self.tri.vertices)
+            r_max = max(self.data[v] for v in self.tri.vertices)
+
+            raise ValueError(
+                f"Could not draw isosurface for level={level}, as"
+                " this value is not inside the function range. Please choose"
+                f" a level strictly inside interval ({r_min}, {r_max})"
+            )
+
+        return vertices, faces
+
+    def plot_isosurface(self, level=0.0, hull_opacity=0.2):
+        """Plots the linearly interpolated isosurface of the function,
+        based on the currently evaluated points. This is the 3D analog
+        of an isoline.
+
+        Parameters
+        ----------
+        level : float, default 0.0
+            the function value which you are interested in.
+        hull_opacity : float, default 0.0
+            the opacity of the hull of the domain.
+
+        Returns
+        -------
+        plot : plotly.offline.iplot object
+            The plot object of the isosurface.
+        """
+        plotly = ensure_plotly()
+
+        vertices, faces = self._get_isosurface(level)
+        x, y, z = zip(*vertices)
+
+        fig = plotly.figure_factory.create_trisurf(
+            x=x, y=y, z=z, plot_edges=False,
+            simplices=faces, title="Isosurface")
+
+        if hull_opacity < 1e-3:
+            # Do not compute the hull_mesh.
+            return plotly.offline.iplot(fig)
+
+        hull_mesh = self._get_hull_mesh(opacity=hull_opacity)
+        return plotly.offline.iplot([fig.data[0], hull_mesh])
+
+    def _get_hull_mesh(self, opacity=0.2):
+        plotly = ensure_plotly()
+        hull = scipy.spatial.ConvexHull(self._bounds_points)
+
+        # Find the colors of each plane, giving triangles which are coplanar
+        # the same color, such that a square face has the same color.
+        color_dict = {}
+
+        def _get_plane_color(simplex):
+            simplex = tuple(simplex)
+            # If the volume of the two triangles combined is zero then they
+            # belong to the same plane.
+            for simplex_key, color in color_dict.items():
+                points = [hull.points[i] for i in set(simplex_key + simplex)]
+                points = np.array(points)
+                if np.linalg.matrix_rank(points[1:] - points[0]) < 3:
+                    return color
+                if scipy.spatial.ConvexHull(points).volume < 1e-5:
+                    return color
+            color_dict[simplex] = tuple(random.randint(0, 255)
+                                        for _ in range(3))
+            return color_dict[simplex]
+
+        colors = [_get_plane_color(simplex) for simplex in hull.simplices]
+
+        x, y, z = zip(*self._bounds_points)
+        i, j, k = hull.simplices.T
+        return plotly.graph_objs.Mesh3d(x=x, y=y, z=z, i=i, j=j, k=k,
+                                        facecolor=colors, opacity=opacity)