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isoline_demo.py
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isoline_demo.py
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""" Code for demo-ing and experimentation. Prepare for a mess """
import os
import cairo
import numpy as np
from isosurfaces import plot_isoline
from isosurfaces.isoline import Cell, CurveTracer, Triangulator, build_tree
min_depth = 5
pmin = np.array([-8, -6])
pmax = np.array([8, 6])
def f(x, y):
return y * (x - y) ** 2 - 4 * x - 8
# Here we directly use plot_implicit internals in order to see the quadtree
fn = lambda u: f(u[0], u[1])
tol = (pmax - pmin) / 1000
quadtree = build_tree(2, fn, pmin, pmax, min_depth, 5000, tol)
triangles = Triangulator(quadtree, fn, tol).triangulate()
curves = CurveTracer(triangles, fn, tol).trace()
def g(x, y):
return x**3 - x - y**2
# Typical usage
curves1 = plot_isoline(
lambda u: g(u[0], u[1]),
pmin,
pmax,
min_depth=4,
max_quads=1000,
)
def h(x, y):
return x**4 + y**4 - np.sin(x) - np.sin(4 * y)
curves2 = plot_isoline(lambda u: h(u[0], u[1]), pmin, pmax, 4, 1000)
def tanm(x, y):
return np.tan(x**2 + y**2) - 1
curves3 = plot_isoline(lambda u: tanm(u[0], u[1]), pmin, pmax, 6, 5000)
WIDTH = 640
HEIGHT = 480
def setup_context(c):
# reflection to change math units to screen units
scale = min(WIDTH / (pmax[0] - pmin[0]), HEIGHT / (pmax[1] - pmin[1]))
c.scale(scale, -scale)
c.translate(WIDTH / scale / 2, -HEIGHT / scale / 2)
c.set_line_join(cairo.LINE_JOIN_BEVEL)
def draw_axes(c):
c.save()
c.set_line_width(0.1)
c.move_to(0, -100)
c.line_to(0, 100)
c.stroke()
c.move_to(-100, 0)
c.line_to(100, 0)
c.stroke()
c.restore()
def draw_quad(c, quad: Cell):
width = 0
if quad.depth <= min_depth:
width = 0.02
elif quad.depth == min_depth + 1:
width = 0.01
else:
width = 0.005
c.set_line_width(0.5 * width)
if quad.children:
c.move_to(*((quad.vertices[0].pos + quad.vertices[1].pos) / 2))
c.line_to(*((quad.vertices[2].pos + quad.vertices[3].pos) / 2))
c.move_to(*((quad.vertices[0].pos + quad.vertices[2].pos) / 2))
c.line_to(*((quad.vertices[1].pos + quad.vertices[3].pos) / 2))
c.stroke()
for child in quad.children:
draw_quad(c, child)
def draw_quads(c):
c.save()
draw_quad(c, quadtree)
c.restore()
def draw_triangles(c):
c.save()
c.set_line_width(0.001)
for tri in triangles:
c.move_to(*tri.vertices[0].pos)
c.line_to(*tri.vertices[1].pos)
c.line_to(*tri.vertices[2].pos)
c.line_to(*tri.vertices[0].pos)
c.stroke()
c.restore()
def draw_signs(c):
c.save()
for tri in triangles:
for vert in tri.vertices:
vert.drawn = False
for tri in triangles:
for vert in tri.vertices:
if vert.drawn:
continue
vert.drawn = True
if vert.val > 0:
c.set_source_rgb(0.2, 0.2, 1)
else:
c.set_source_rgb(1, 0.2, 0.2)
w = 0.01
c.rectangle(vert.pos[0] - w, vert.pos[1] - w, 2 * w, 2 * w)
c.fill()
c.restore()
def draw_bg(c):
c.save()
c.set_source_rgb(1, 1, 1)
c.paint()
c.restore()
def draw_curves(c, curves_list, rgb):
print("drawing", sum(map(len, curves_list)), "segments in", len(curves_list), "curves")
c.set_source_rgb(*rgb)
# draw curves
c.save()
c.set_line_width(0.03)
for curve in curves_list:
c.move_to(*curve[0])
for v in curve[1:]:
c.line_to(*v)
c.stroke()
c.restore()
def draw_curve_vertices(c, curves_list, rgb):
c.set_source_rgb(*rgb)
c.save()
w = 0.01
for curve in curves_list:
for v in curve:
c.rectangle(v[0] - w, v[1] - w, 2 * w, 2 * w)
c.fill()
c.restore()
if not os.path.exists("out"):
os.mkdir("out")
with cairo.SVGSurface("out/demo.svg", WIDTH, HEIGHT) as surface:
c = cairo.Context(surface)
setup_context(c)
draw_bg(c)
draw_axes(c)
# draw_quads(c)
# draw_triangles(c)
# draw_signs(c)
draw_curves(c, curves, [0.1, 0.1, 0.8])
# draw_curve_vertices(c, curves, [0.5, 0.8, 0.6])
draw_curves(c, curves1, [0.8, 0.1, 0.1])
draw_curves(c, curves2, [0.1, 0.6, 0.1])
# draw_curves(c, curves3, [0.1, 0.4, 0.5])