223 lines
6.4 KiB
Cython
223 lines
6.4 KiB
Cython
# cython: language_level=3
|
|
# Copyright (c) 2021-2024 Manfred Moitzi
|
|
# License: MIT License
|
|
from typing import TYPE_CHECKING, Sequence
|
|
from .vector cimport Vec3, isclose, v3_dist, v3_lerp, v3_add, Vec2
|
|
from .matrix44 cimport Matrix44
|
|
import warnings
|
|
if TYPE_CHECKING:
|
|
from ezdxf.math import UVec
|
|
|
|
__all__ = ['Bezier3P']
|
|
|
|
cdef extern from "constants.h":
|
|
const double ABS_TOL
|
|
const double REL_TOL
|
|
|
|
cdef double RECURSION_LIMIT = 1000
|
|
|
|
|
|
cdef class Bezier3P:
|
|
cdef:
|
|
FastQuadCurve curve # pyright: ignore
|
|
readonly Vec3 start_point
|
|
Vec3 cp1
|
|
readonly Vec3 end_point
|
|
|
|
def __cinit__(self, defpoints: Sequence[UVec]):
|
|
if not isinstance(defpoints[0], (Vec2, Vec3)):
|
|
warnings.warn(
|
|
DeprecationWarning,
|
|
"Bezier3P requires defpoints of type Vec2 or Vec3 in the future",
|
|
)
|
|
if len(defpoints) == 3:
|
|
self.start_point = Vec3(defpoints[0])
|
|
self.cp1 = Vec3(defpoints[1])
|
|
self.end_point = Vec3(defpoints[2])
|
|
|
|
self.curve = FastQuadCurve(
|
|
self.start_point,
|
|
self.cp1,
|
|
self.end_point
|
|
)
|
|
else:
|
|
raise ValueError("Three control points required.")
|
|
|
|
@property
|
|
def control_points(self) -> tuple[Vec3, Vec3, Vec3]:
|
|
return self.start_point, self.cp1, self.end_point
|
|
|
|
def __reduce__(self):
|
|
return Bezier3P, (self.control_points,)
|
|
|
|
def point(self, double t) -> Vec3:
|
|
if 0.0 <= t <= 1.0:
|
|
return self.curve.point(t)
|
|
else:
|
|
raise ValueError("t not in range [0 to 1]")
|
|
|
|
def tangent(self, double t) -> Vec3:
|
|
if 0.0 <= t <= 1.0:
|
|
return self.curve.tangent(t)
|
|
else:
|
|
raise ValueError("t not in range [0 to 1]")
|
|
|
|
def approximate(self, int segments) -> list[Vec3]:
|
|
cdef double delta_t
|
|
cdef int segment
|
|
cdef list points = [self.start_point]
|
|
|
|
if segments < 1:
|
|
raise ValueError(segments)
|
|
delta_t = 1.0 / segments
|
|
for segment in range(1, segments):
|
|
points.append(self.point(delta_t * segment))
|
|
points.append(self.end_point)
|
|
return points
|
|
|
|
def flattening(self, double distance, int segments = 4) -> list[Vec3]:
|
|
cdef double dt = 1.0 / segments
|
|
cdef double t0 = 0.0, t1
|
|
cdef _Flattening f = _Flattening(self, distance)
|
|
cdef Vec3 start_point = self.start_point
|
|
cdef Vec3 end_point
|
|
while t0 < 1.0:
|
|
t1 = t0 + dt
|
|
if isclose(t1, 1.0, REL_TOL, ABS_TOL):
|
|
end_point = self.end_point
|
|
t1 = 1.0
|
|
else:
|
|
end_point = self.curve.point(t1)
|
|
f.reset_recursion_check()
|
|
f.flatten(start_point, end_point, t0, t1)
|
|
if f.has_recursion_error():
|
|
raise RecursionError(
|
|
"Bezier3P flattening error, check for very large coordinates"
|
|
)
|
|
t0 = t1
|
|
start_point = end_point
|
|
return f.points
|
|
|
|
def approximated_length(self, segments: int = 128) -> float:
|
|
cdef double length = 0.0
|
|
cdef bint start_flag = 0
|
|
cdef Vec3 prev_point, point
|
|
|
|
for point in self.approximate(segments):
|
|
if start_flag:
|
|
length += v3_dist(prev_point, point)
|
|
else:
|
|
start_flag = 1
|
|
prev_point = point
|
|
return length
|
|
|
|
def reverse(self) -> Bezier3P:
|
|
return Bezier3P((self.end_point, self.cp1, self.start_point))
|
|
|
|
def transform(self, Matrix44 m) -> Bezier3P:
|
|
return Bezier3P(tuple(m.transform_vertices(self.control_points)))
|
|
|
|
|
|
cdef class _Flattening:
|
|
cdef FastQuadCurve curve # pyright: ignore
|
|
cdef double distance
|
|
cdef list points
|
|
cdef int _recursion_level
|
|
cdef int _recursion_error
|
|
|
|
def __cinit__(self, Bezier3P curve, double distance):
|
|
self.curve = curve.curve
|
|
self.distance = distance
|
|
self.points = [curve.start_point]
|
|
self._recursion_level = 0
|
|
self._recursion_error = 0
|
|
|
|
cdef has_recursion_error(self):
|
|
return self._recursion_error
|
|
|
|
cdef reset_recursion_check(self):
|
|
self._recursion_level = 0
|
|
self._recursion_error = 0
|
|
|
|
cdef flatten(
|
|
self,
|
|
Vec3 start_point,
|
|
Vec3 end_point,
|
|
double start_t,
|
|
double end_t
|
|
):
|
|
if self._recursion_level > RECURSION_LIMIT:
|
|
self._recursion_error = 1
|
|
return
|
|
self._recursion_level += 1
|
|
cdef double mid_t = (start_t + end_t) * 0.5
|
|
cdef Vec3 mid_point = self.curve.point(mid_t)
|
|
cdef double d = v3_dist(mid_point, v3_lerp(start_point, end_point, 0.5))
|
|
if d < self.distance:
|
|
self.points.append(end_point)
|
|
else:
|
|
self.flatten(start_point, mid_point, start_t, mid_t)
|
|
self.flatten(mid_point, end_point, mid_t, end_t)
|
|
self._recursion_level -= 1
|
|
|
|
|
|
cdef class FastQuadCurve:
|
|
cdef:
|
|
double[3] offset
|
|
double[3] p1
|
|
double[3] p2
|
|
|
|
def __cinit__(self, Vec3 p0, Vec3 p1, Vec3 p2):
|
|
self.offset[0] = p0.x
|
|
self.offset[1] = p0.y
|
|
self.offset[2] = p0.z
|
|
|
|
# 1st control point (p0) is always (0, 0, 0)
|
|
self.p1[0] = p1.x - p0.x
|
|
self.p1[1] = p1.y - p0.y
|
|
self.p1[2] = p1.z - p0.z
|
|
|
|
self.p2[0] = p2.x - p0.x
|
|
self.p2[1] = p2.y - p0.y
|
|
self.p2[2] = p2.z - p0.z
|
|
|
|
|
|
cdef Vec3 point(self, double t):
|
|
# 1st control point (p0) is always (0, 0, 0)
|
|
# => p0 * a is always (0, 0, 0)
|
|
cdef:
|
|
Vec3 result = Vec3()
|
|
# double a = (1 - t) ** 2
|
|
double b = 2.0 * t * (1.0 - t)
|
|
double c = t * t
|
|
|
|
iadd_mul(result, self.p1, b)
|
|
iadd_mul(result, self.p2, c)
|
|
|
|
# add offset at last - it is maybe very large
|
|
result.x += self.offset[0]
|
|
result.y += self.offset[1]
|
|
result.z += self.offset[2]
|
|
|
|
return result
|
|
|
|
|
|
cdef Vec3 tangent(self, double t):
|
|
# tangent vector is independent from offset location!
|
|
cdef:
|
|
Vec3 result = Vec3()
|
|
# double a = -2 * (1 - t)
|
|
double b = 2.0 - 4.0 * t
|
|
double c = 2.0 * t
|
|
|
|
iadd_mul(result, self.p1, b)
|
|
iadd_mul(result, self.p2, c)
|
|
|
|
return result
|
|
|
|
|
|
cdef void iadd_mul(Vec3 a, double[3] b, double c):
|
|
a.x += b[0] * c
|
|
a.y += b[1] * c
|
|
a.z += b[2] * c
|