858 lines
27 KiB
Python
858 lines
27 KiB
Python
import enum
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import io
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import obja.obja as obja
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import numpy as np
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import argparse
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from rich.progress import Progress
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def cot(x: float) -> float:
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"""Cotangeante of x
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Args:
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x (float): angle
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Returns:
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float: cotangeante of x
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"""
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sin_x = np.sin(x)
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if sin_x == 0:
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return 1e16
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return np.cos(x) / sin_x
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def sliding_window(l: list, n: int = 2) -> list[tuple]:
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"""Create a sliding window of size n
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Args:
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l (list): list to create the sliding window from
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n (int, optional): number of value. Defaults to 2.
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Returns:
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list[tuple]: sliding window
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"""
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k = n - 1
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l2 = l + [l[i] for i in range(k)]
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res = [(x for x in l2[i:i+n]) for i in range(len(l2)-k)]
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return res
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class Edge:
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"""Edge representation"""
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def __init__(self, a: int, b: int) -> None:
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"""Create an edge
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Args:
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a (int): first vertex
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b (int): second vertex
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"""
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self.a = min(a, b)
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self.b = max(a, b)
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self.face1: Face | None = None
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self.face2: Face | None = None
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self.fold: float = 0.0
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self.curvature: float = 0.0
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def __eq__(self, __o: object) -> bool:
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"""Check if two edges are equal
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Args:
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__o (object): other edge
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Returns:
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bool: True if equal, False otherwise
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"""
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if isinstance(__o, Edge):
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return self.a == __o.a and self.b == __o.b
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return False
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class Face:
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"""Face representation"""
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def __init__(self, a: int, b: int, c: int) -> None:
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"""Face constructor
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Args:
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a (int): first vertex index
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b (int): second vertex index
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c (int): third vertex index
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"""
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self.a = a
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self.b = b
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self.c = c
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self.edges: list[Edge] = []
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self.a = a
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self.b = b
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self.c = c
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self.normal = np.zeros(3)
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def to_obja(self) -> obja.Face:
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"""Convert face to obja format
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Returns:
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obja.Face: face in obja format
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"""
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return obja.Face(self.a, self.b, self.c)
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def __eq__(self, __o: object) -> bool:
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"""Check if two faces are equal
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Args:
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__o (object): other face
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Returns:
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bool: True if equal, False otherwise
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"""
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if isinstance(__o, Face):
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return set((__o.a, __o.b, __o.c)) == set((self.a, self.b, self.c))
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return False
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class Vertex:
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"""Vertex representation"""
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def __init__(self, pos: np.ndarray[int, float]) -> None:
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"""Vertex constructor
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Args:
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pos (np.ndarray[int, float]): position of the vertex
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"""
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self.pos = pos
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self.vertex_ring: list[int] = []
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self.face_ring: list[int] = []
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self.normal: np.ndarray = np.zeros(3)
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self.area: float = 0.0
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self.curvature: float = 0.0
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def to_obja(self) -> np.ndarray:
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"""Convert vertex to obja format
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Returns:
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np.ndarray: vertex in obja format
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"""
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return self.pos
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class MAPS(obja.Model):
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"""MAPS compression model"""
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def __init__(self):
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"""MAPS constructor"""
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super().__init__()
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def parse_file(self, path: str) -> None:
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"""Parse a file
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Args:
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path (str): path to the file
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"""
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super().parse_file(path)
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for i, vertex in enumerate(self.vertices):
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self.vertices[i] = Vertex(vertex)
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for i, face in enumerate(self.faces):
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self.faces[i] = Face(face.a, face.b, face.c)
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def update(self) -> None:
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"""Precompute things"""
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# Reset progress bars
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self.progress.reset(self.select_task, total=len(self.vertices))
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self.progress.reset(self.compress_task)
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# Compute usefull things
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self.update_rings()
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self.update_edges()
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self.update_normals()
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self.update_area_curvature()
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def fix(self) -> None:
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"""Fix the model"""
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fixed = True
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# Find a vertex with less than 3 faces
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for i, vertex in enumerate(self.vertices):
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if vertex is None:
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continue
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if len(vertex.face_ring) < 3:
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# Remove the vertex and its faces
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for face in vertex.face_ring:
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if not self.final_only:
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self.operations.append(
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('af', face, self.faces[face].to_obja()))
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self.faces[face] = None
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if not self.final_only:
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self.operations.append(
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('av', i, vertex.to_obja()))
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self.vertices[i] = None
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# Indicate that the model has to be fixed again
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fixed = False
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return fixed
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def update_edges(self) -> None:
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"""Update edges"""
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self.edges = {}
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for face in self.faces:
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if face is None:
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continue
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# Create all edges for the face
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for a, b in sliding_window([face.a, face.b, face.c], n=2):
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new_edge = Edge(a, b)
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# Check if the edge already exists
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if f"{new_edge.a}:{new_edge.b}" in self.edges.keys():
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continue
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new_edge.face1 = face
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# Find the opoosite face
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for face2_i in self.vertices[new_edge.a].face_ring:
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face2 = self.faces[face2_i]
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if face2 == face:
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continue
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face2_vertices = (face2.a, face2.b, face2.c)
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if not (a in face2_vertices and b in face2_vertices):
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continue
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new_edge.face2 = face2
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break
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# Add the new edge to the list
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self.edges[f"{new_edge.a}:{new_edge.b}"] = new_edge
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def update_rings(self) -> None:
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"""Update vertex and face rings"""
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fixed = False
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# Wait till the model is fixed
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while not fixed:
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for vertex in self.vertices:
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# Reset vertex ring
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if vertex is None:
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continue
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vertex.face_ring = []
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# Add faces to vertex ring
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for i, face in enumerate(self.faces):
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if face is None:
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continue
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for vertex_i in (face.a, face.b, face.c):
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self.vertices[vertex_i].face_ring.append(i)
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# Fix the model
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fixed = self.fix()
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for i, vertex in enumerate(self.vertices):
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vertex = self.vertices[i]
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if vertex is None:
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continue
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# Compute rings
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ring = self.one_ring(i)
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vertex.vertex_ring = ring
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def update_area_curvature(self) -> None:
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"""Update area and curvature"""
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# Get the area and curvature of each vertex
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for i, vertex in enumerate(self.vertices):
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if vertex is None:
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continue
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area, curvature = self.compute_area_curvature(i)
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vertex.area = area
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vertex.curvature = curvature
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# Find feature edges
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self.feature_edges = []
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for edge in self.edges.values():
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edge.fold = np.dot(edge.face1.normal, edge.face2.normal)
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if edge.fold < 0.5:
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self.feature_edges.append(edge)
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def update_normals(self) -> None:
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"""Update normals"""
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for face in self.faces:
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if face is None:
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continue
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# Compute face normal
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p1 = self.vertices[face.a].pos
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p2 = self.vertices[face.b].pos
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p3 = self.vertices[face.c].pos
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u = p2 - p1
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v = p3 - p1
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n = np.cross(u, v)
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norm = np.linalg.norm(n)
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if norm != 0:
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n /= np.linalg.norm(n)
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face.normal = n
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# Sum vertex normal
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self.vertices[face.a].normal += n
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self.vertices[face.b].normal += n
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self.vertices[face.c].normal += n
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# Normalize vertex normals
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for vertex in self.vertices:
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if vertex is None:
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continue
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norm = np.linalg.norm(vertex.normal)
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if norm != 0:
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vertex.normal /= norm
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def one_ring(self, index: int) -> list[int]:
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"""Return the corresponding 1-ring
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Args:
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index (int): index of the 1-ring's main vertex
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Returns:
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list[int]: ordered list of the 1-ring vertices
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"""
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ring_faces = [self.faces[i] for i in self.vertices[index].face_ring]
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# Initialize the ring
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start_index = (ring_faces[0].a if ring_faces[0].a != index and ring_faces[0].c != index else
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ring_faces[0].b if ring_faces[0].a != index and ring_faces[0].b != index else
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ring_faces[0].c)
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ring = [start_index]
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ring_faces.pop(0)
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# Select the indexes of the ring in the right order
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while len(ring_faces) > 0:
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broke = False
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prev_index = ring[-1]
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for i, face in enumerate(ring_faces):
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if prev_index in (face.a, face.b, face.c):
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# Found the face that correspond to the next vertex
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current_index = ( # select the next vertex from the face
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face.a if face.a != index and face.a != prev_index else
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face.b if face.b != index and face.b != prev_index else
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face.c
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)
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ring.append(current_index)
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ring_faces.pop(i)
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broke = True
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break
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if not broke:
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raise Exception('Ring not corrupted')
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return ring
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def compute_area_curvature(self, index: int) -> tuple[float, float]:
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"""Compute area and curvature the corresponding 1-ring
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Args:
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index (int): index of the 1-ring's main vertex
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Returns:
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tuple[float, float]: area and curvature
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"""
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ring = self.vertices[index].vertex_ring
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p1 = self.vertices[index].pos
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n1 = self.vertices[index].normal
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area_sum = 0
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curvature = 0
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for index1, index2 in sliding_window(ring, n=2):
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# the second vertice of the triangle
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p2 = self.vertices[index1].pos
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p3 = self.vertices[index2].pos # the third vertice of the triangle
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n2 = self.vertices[index1].normal
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M = np.array([ # build the matrix, used to compute the area
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[p1[0], p2[0], p3[0]],
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[p1[1], p2[1], p3[1]],
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[p1[2], p2[2], p3[2]],
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])
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area = abs(np.linalg.det(M) / 2) # compute the area
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area_sum += area
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edge_curvature = np.dot(n2 - n1, p2 - p1) / \
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np.linalg.norm(p2 - p1)**2
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edge_curvature = abs(edge_curvature)
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edge_key = f"{min(index, index1)}:{max(index, index1)}"
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self.edges[edge_key].curvature = edge_curvature
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curvature += edge_curvature
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curvature /= len(ring)
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return area_sum, curvature
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def compute_priority(self, lamb: float = 0.5, max_length: int = 12) -> list[float]:
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""" Compute selection priority of vertices (0.0 -> hight priority ; 1.0 -> low priority)
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Args:
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lamb (float, optional): convex combination factor. Defaults to 0.5.
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max_length (int, optional): 1-ring maximum length to be prioritary. Defaults to 12.
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Returns:
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list[float]: priority values
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"""
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max_area = max(
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[vertex.area for vertex in self.vertices if vertex is not None])
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max_curvature = max(
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[vertex.curvature for vertex in self.vertices if vertex is not None])
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# Compute priorities
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priorities = []
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for vertex in self.vertices:
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if vertex is not None and len(vertex.vertex_ring) < max_length:
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# Compute priority
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priority = (
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lamb * vertex.area / max_area +
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(1.0 - lamb) * vertex.curvature / max_curvature
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)
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else:
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# Vertex with low priority
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priority = 2.0
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priorities.append(priority)
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return priorities
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def select_vertices(self) -> list[int]:
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""" Select vertices for the current level reduction
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Returns:
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list[int]: selected vertices
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"""
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# Order vertices by priority
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priorities = self.compute_priority()
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vertices = [i[0]
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for i in sorted(enumerate(priorities), key=lambda p: p[1])]
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selected_vertices = []
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while len(vertices) > 0:
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# Select prefered vertex
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vertex = vertices.pop(0) # remove it from remaining vertices
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self.progress.advance(self.select_task)
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if priorities[vertex] == 2.0:
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continue
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incident_count = 0
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for feature_edge in self.feature_edges:
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if vertex in (feature_edge.a, feature_edge.b):
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incident_count += 1
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if incident_count > 2:
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continue
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selected_vertices.append(vertex)
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# Remove neighbors
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# for face in remaining_faces:
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for face in self.faces:
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if face is None:
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continue
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face_vertices = (face.a, face.b, face.c)
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if vertex in face_vertices:
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# Remove face and face's vertices form remainings
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# remaining_faces.remove(face)
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for face_vertex in face_vertices:
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if face_vertex in vertices:
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vertices.remove(face_vertex)
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self.progress.advance(self.select_task)
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return selected_vertices
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def project_polar(self, index: int) -> tuple[list[np.ndarray], list[int]]:
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"""Flatten the 1-ring to retriangulate
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Args:
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index (int): main vertex of the 1-ring
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Returns:
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list[np.ndarray]: list the cartesian coordinates of the flattened 1-ring projected in the plane
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"""
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ring = self.vertices[index].vertex_ring
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radius, angles = [], []
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teta = 0.0 # cumulated angles
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for index1, index2 in sliding_window(ring):
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r = np.linalg.norm(
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self.vertices[index].pos - self.vertices[index1].pos)
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teta += self.compute_angle(index1, index, index2) # add new angle
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radius.append(r)
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angles.append(teta)
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angles = [2 * np.pi * a / teta for a in angles] # normalize angles
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coordinates = [np.array([r * np.cos(a), r * np.sin(a)])
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for r, a in zip(radius, angles)] # parse polar to cartesian
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return coordinates, ring
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def compute_angle(self, i: int, j: int, k: int) -> float:
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"""Calculate the angle defined by three points
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Args:
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i (int): previous index
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j (int): central index
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k (int): next index
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Returns:
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float: angle defined by the three points
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"""
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a = self.vertices[i].pos
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b = self.vertices[j].pos
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c = self.vertices[k].pos
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u = a - b
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v = c - b
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u /= np.linalg.norm(u)
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v /= np.linalg.norm(v)
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res = np.dot(u, v)
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return np.arccos(np.clip(res, -1, 1))
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def clip_ear(self, index: int) -> list[obja.Face]:
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"""Retriangulate a polygon using the ear clipping algorithm
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Args:
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index (int): index of 1-ring
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Returns:
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tuple[list[obja.Face], int]: list the triangles
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"""
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polygon_, ring_ = self.project_polar(index)
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main_v = []
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for i, r in enumerate(ring_):
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for feature_edge in self.feature_edges:
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feat_edge_vertices = (feature_edge.a, feature_edge.b)
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if r in feat_edge_vertices and index in feat_edge_vertices:
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main_v.append(i)
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if len(main_v) < 2:
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polygons_rings = [(polygon_, ring_)]
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else:
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v1 = ring_[main_v[0]]
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v2 = ring_[main_v[1]]
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ring1, ring2 = [], []
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polygon1, polygon2, = [], []
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start = ring_.index(v1)
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while ring_[start] != v2:
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ring1.append(ring_[start])
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polygon1.append(polygon_[start])
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start += 1
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start %= len(ring_)
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ring1.append(ring_[start])
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polygon1.append(polygon_[start])
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start = ring_.index(v2)
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while ring_[start] != v1:
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ring2.append(ring_[start])
|
|
polygon2.append(polygon_[start])
|
|
start += 1
|
|
start %= len(ring_)
|
|
ring2.append(ring_[start])
|
|
polygon2.append(polygon_[start])
|
|
|
|
polygons_rings = [(polygon1, ring1), (polygon2, ring2)]
|
|
|
|
faces = [] # the final list of faces
|
|
|
|
for polygon, ring in polygons_rings:
|
|
|
|
indices = [(local_i, global_i)
|
|
for local_i, global_i in enumerate(ring)] # remainging vertices
|
|
|
|
node_index = 0
|
|
cycle_counter = 0
|
|
while len(indices) > 2:
|
|
# Extract indices
|
|
local_i, global_i = indices[node_index - 1]
|
|
local_j, global_j = indices[node_index]
|
|
local_k, global_k = indices[node_index + 1]
|
|
|
|
# Extract verticies
|
|
prev_vert = polygon[local_i]
|
|
curr_vert = polygon[local_j]
|
|
next_vert = polygon[local_k]
|
|
|
|
is_convex = self.is_convex(prev_vert, curr_vert, next_vert)
|
|
is_ear = True
|
|
# the triangle needs to be convext to be an ear
|
|
if is_convex or cycle_counter > len(indices):
|
|
# Begin with the point next to the triangle
|
|
test_node_index = (node_index + 2) % len(indices)
|
|
while indices[test_node_index][0] != local_i and is_ear:
|
|
test_vert = polygon[indices[test_node_index][0]]
|
|
is_ear = not self.is_inside(prev_vert,
|
|
curr_vert,
|
|
next_vert,
|
|
test_vert)
|
|
test_node_index = (test_node_index + 1) % len(indices)
|
|
else:
|
|
is_ear = False
|
|
cycle_counter += 1
|
|
|
|
if is_ear:
|
|
faces.append(Face(global_i, global_j, global_k))
|
|
indices.pop(node_index) # remove the point from the ring
|
|
cycle_counter = 0
|
|
|
|
node_index = (node_index + 2) % len(indices) - 1
|
|
|
|
return faces
|
|
|
|
def is_convex(self,
|
|
prev_vert: np.ndarray[int, float],
|
|
curr_vert: np.ndarray[int, float],
|
|
next_vert: np.ndarray[int, float],
|
|
) -> bool:
|
|
"""Check if the angle less than pi
|
|
|
|
Args:
|
|
prev_vert (np.ndarray): first point
|
|
curr_vert (np.ndarray): middle point
|
|
next_vert (np.ndarray): last point
|
|
|
|
Returns:
|
|
bool: angle smaller than pi
|
|
"""
|
|
a = prev_vert - curr_vert
|
|
b = next_vert - curr_vert
|
|
dot = a[0] * b[0] + a[1] * b[1]
|
|
det = a[0] * b[1] - a[1] * b[0]
|
|
angle = np.arctan2(det, dot)
|
|
if angle < 0.0:
|
|
angle = 2.0 * np.pi + angle
|
|
internal_angle = angle
|
|
return internal_angle >= np.pi
|
|
|
|
def is_inside(self,
|
|
a: np.ndarray[int, float],
|
|
b: np.ndarray[int, float],
|
|
c: np.ndarray[int, float],
|
|
p: np.ndarray[int, float],
|
|
) -> bool:
|
|
"""Check if p is in the triangle a b c
|
|
|
|
Args:
|
|
a (np.ndarray): point one
|
|
b (np.ndarray): point two
|
|
c (np.ndarray): point three
|
|
p (np.ndarray): point to check
|
|
|
|
Returns:
|
|
bool: if the point to check is in a b c
|
|
"""
|
|
# Compute vectors
|
|
v0 = c - a
|
|
v1 = b - a
|
|
v2 = p - a
|
|
|
|
# Compute dot products
|
|
dot00 = np.dot(v0, v0)
|
|
dot01 = np.dot(v0, v1)
|
|
dot02 = np.dot(v0, v2)
|
|
dot11 = np.dot(v1, v1)
|
|
dot12 = np.dot(v1, v2)
|
|
|
|
# Compute barycentric coordinates
|
|
denom = dot00 * dot11 - dot01 * dot01
|
|
if abs(denom) < 1e-20:
|
|
return True
|
|
invDenom = 1.0 / denom
|
|
u = (dot11 * dot02 - dot01 * dot12) * invDenom
|
|
v = (dot00 * dot12 - dot01 * dot02) * invDenom
|
|
|
|
# Check if point is in triangle
|
|
return (u >= 0) and (v >= 0) and (u + v < 1)
|
|
|
|
def debug(self, output):
|
|
|
|
self.update()
|
|
priorities = self.compute_priority()
|
|
|
|
colors = [priorities[face.a] + priorities[face.b] +
|
|
priorities[face.c] if face is not None else 0.0 for face in self.faces]
|
|
min_c = min(colors)
|
|
colors = [c - min_c for c in colors]
|
|
max_c = max(colors)
|
|
|
|
self.operations = []
|
|
for i, face in enumerate(self.faces):
|
|
if face is None:
|
|
continue
|
|
r, g, b = colors[i] / max_c, 1.0, 1.0
|
|
|
|
for feature_edge in self.feature_edges:
|
|
face_vertices = (face.a, face.b, face.c)
|
|
if feature_edge.a in face_vertices and feature_edge.b in face_vertices:
|
|
r, g, b = 1.0, 0.0, 0.0
|
|
break
|
|
|
|
self.operations.append(('fc', i, (r, g, b)))
|
|
self.operations.append(('af', i, face.to_obja()))
|
|
|
|
for i, vertex in enumerate(self.vertices):
|
|
if vertex is None:
|
|
continue
|
|
self.operations.append(('av', i, vertex.to_obja()))
|
|
self.operations.reverse()
|
|
|
|
# Write the result in output file
|
|
output_model = obja.Output(output)
|
|
|
|
for (op, index, value) in self.operations:
|
|
if op == 'av':
|
|
output_model.add_vertex(index, value)
|
|
elif op == 'af':
|
|
output_model.add_face(index, value)
|
|
elif op == 'ev':
|
|
output_model.edit_vertex(index, value)
|
|
elif op == 'ef':
|
|
output_model.edit_face(index, value)
|
|
elif op == 'fc':
|
|
print('fc {} {} {} {}'.format(
|
|
len(output_model.face_mapping),
|
|
value[0],
|
|
value[1],
|
|
value[2]),
|
|
file=output
|
|
)
|
|
|
|
def compress(self, output: io.TextIOWrapper, level: int, final_only: bool, debug: bool) -> None:
|
|
"""Compress the 3d model
|
|
|
|
Args:
|
|
output (io.TextIOWrapper): Output file descriptor
|
|
"""
|
|
|
|
with Progress() as progress:
|
|
self.global_task = progress.add_task('╓ Global compression')
|
|
self.select_task = progress.add_task('╟── Vertex selection')
|
|
self.compress_task = progress.add_task('╙── Compression')
|
|
self.progress = progress
|
|
|
|
self.operations = []
|
|
self.final_only = final_only
|
|
|
|
# while len(self.vertices) > 64:
|
|
for _ in progress.track(range(level), task_id=self.global_task):
|
|
self.update()
|
|
selected_vertices = self.select_vertices() # find the set of vertices to remove
|
|
|
|
for v_index in self.progress.track(selected_vertices, task_id=self.compress_task):
|
|
|
|
# Extract ring faces
|
|
ring_faces = self.vertices[v_index].face_ring
|
|
|
|
# Apply retriangulation algorithm
|
|
faces = self.clip_ear(v_index)
|
|
|
|
# Edit the first faces
|
|
for i in range(len(faces)):
|
|
if not self.final_only:
|
|
self.operations.append(
|
|
('ef', ring_faces[i], self.faces[ring_faces[i]].to_obja()))
|
|
self.faces[ring_faces[i]] = faces[i]
|
|
|
|
# Remove the last faces
|
|
for i in range(len(faces), len(ring_faces)):
|
|
if not self.final_only:
|
|
self.operations.append(
|
|
('af', ring_faces[i], self.faces[ring_faces[i]].to_obja()))
|
|
self.faces[ring_faces[i]] = None
|
|
|
|
# Remove the vertex
|
|
if not self.final_only:
|
|
self.operations.append(
|
|
('av', v_index, self.vertices[v_index].to_obja()))
|
|
self.vertices[v_index] = None
|
|
|
|
if debug:
|
|
self.debug(output)
|
|
return
|
|
|
|
# Register remaining vertices and faces
|
|
for i, face in enumerate(self.faces):
|
|
if face is not None:
|
|
self.operations.append(('af', i, face.to_obja()))
|
|
for i, v_index in enumerate(self.vertices):
|
|
if v_index is not None:
|
|
self.operations.append(('av', i, v_index.to_obja()))
|
|
|
|
# To rebuild the model, run operations in reverse order
|
|
self.operations.reverse()
|
|
|
|
# Write the result in output file
|
|
output_model = obja.Output(output)
|
|
|
|
for (op, index, value) in self.operations:
|
|
if op == 'av':
|
|
output_model.add_vertex(index, value)
|
|
elif op == 'af':
|
|
try:
|
|
output_model.add_face(index, value)
|
|
except:
|
|
print(self.vertices[value.b])
|
|
elif op == 'ev':
|
|
output_model.edit_vertex(index, value)
|
|
elif op == 'ef':
|
|
output_model.edit_face(index, value)
|
|
elif op == 'fc':
|
|
print('fc {} {} {} {}'.format(
|
|
index,
|
|
value[0],
|
|
value[1],
|
|
value[2]),
|
|
file=output
|
|
)
|
|
|
|
|
|
def main(args):
|
|
"""Run MAPS model compression
|
|
|
|
Args:
|
|
args (Namespace): arguments (input and output path)
|
|
"""
|
|
model = MAPS()
|
|
model.parse_file(args.input)
|
|
|
|
with open(args.output, 'w') as output:
|
|
model.compress(output, args.level,
|
|
args.final or args.debug, args.debug)
|
|
|
|
|
|
if __name__ == '__main__':
|
|
|
|
parser = argparse.ArgumentParser()
|
|
parser.add_argument('-i', '--input', type=str, required=True)
|
|
parser.add_argument('-o', '--output', type=str, required=True)
|
|
parser.add_argument('-l', '--level', type=int, required=True)
|
|
parser.add_argument('-f', '--final', type=bool, default=False)
|
|
parser.add_argument('-d', '--debug', type=bool, default=False)
|
|
args = parser.parse_args()
|
|
|
|
main(args)
|