# conics - Python library for dealing with conics
#
# Copyright 2026 Sergiu Deitsch <sergiu.deitsch@gmail.com>
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#   http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""
Conic-line intersections
========================

This example computes the intersections of a line with several pairs of
conics: two overlapping circles, two circles touching at a single point, and
two ellipses sharing the same center but with different orientations.
"""

from conics import Conic
from conics.geometry import hnormalized
from matplotlib.patches import Ellipse
import matplotlib.pyplot as plt
import numpy as np


def as_ellipse(c, **kwargs):
    x0, major_minor, angle = c.to_ellipse()
    return Ellipse(
        x0.ravel(), *major_minor.ravel() * 2, angle=np.rad2deg(angle), **kwargs
    )


c1 = Conic.from_circle([0.5, -1], 1)
c2 = c1.translate([0.5, 0]).scale(1.1)

e1 = Conic.from_ellipse([0, 0], [2, 1], np.pi / 4)
e2 = Conic.from_ellipse([0, 0], [2, 1], np.pi * 3 / 4)

c3 = Conic.from_circle([0, 0], 1)
c4 = c3.translate([2 * 1, 0])

alpha = np.deg2rad(-45)
l = np.array([np.cos(alpha), np.sin(alpha), 0])

x = np.linspace(-2, 2)
y = np.linspace(-2, 2)

X, Y = np.meshgrid(x, y)
Z_l = np.dot(np.dstack([X, Y]), l[:-1]) + l[-1]

inter11 = hnormalized(c1.intersect_line(l))
inter12 = hnormalized(c2.intersect_line(l))

inter21 = hnormalized(c3.intersect_line(l))
inter22 = hnormalized(c4.intersect_line(l))

inter31 = hnormalized(e1.intersect_line(l))
inter32 = hnormalized(e2.intersect_line(l))

fig = plt.figure()
ax1, ax2, ax3 = fig.subplots(1, 3)

ax1.set_title('Circles-line')
ax1.add_patch(as_ellipse(c1, facecolor='none', edgecolor='red'))
ax1.add_patch(as_ellipse(c2, facecolor='none', edgecolor='blue'))
ax1.contour(X, Y, Z_l, levels=[0])
ax1.scatter(*inter11.T)
ax1.scatter(*inter12.T)

ax2.set_title('Circles-line')
ax2.add_patch(as_ellipse(c3, facecolor='none', edgecolor='red'))
ax2.add_patch(as_ellipse(c4, facecolor='none', edgecolor='blue'))
ax2.contour(X, Y, Z_l, levels=[0])
ax2.scatter(*inter21.T)

ax3.set_title('Ellipses-line')
ax3.add_patch(as_ellipse(e1, facecolor='none', edgecolor='red'))
ax3.add_patch(as_ellipse(e2, facecolor='none', edgecolor='blue'))
ax3.contour(X, Y, Z_l, levels=[0])
ax3.scatter(*inter31.T)
ax3.scatter(*inter32.T)

ax1.axis('equal')
ax2.axis('equal')

plt.show()