sketch-a-day/2020/sketch_2020_08_20a/arcs.py

172 wiersze
5.5 KiB
Python

# -*- coding: utf-8 -*-
ROTATION = {0: 0,
BOTTOM: 0,
DOWN: 0,
1: HALF_PI,
LEFT: HALF_PI,
2: PI,
TOP: PI,
UP: PI,
3: PI + HALF_PI,
RIGHT: PI + HALF_PI,
BOTTOM + RIGHT: 0,
DOWN + RIGHT: 0,
DOWN + LEFT: HALF_PI,
BOTTOM + LEFT: HALF_PI,
TOP + LEFT: PI,
UP + LEFT: PI,
TOP + RIGHT: PI + HALF_PI,
UP + RIGHT: PI + HALF_PI,
}
def quarter_circle(x, y, radius, quadrant):
circle_arc(x, y, radius, ROTATION[quadrant], HALF_PI)
def half_circle(x, y, radius, quadrant):
circle_arc(x, y, radius, ROTATION[quadrant], PI)
def circle_arc(x, y, radius, start_ang, sweep_ang):
arc(x, y, radius * 2, radius * 2, start_ang, start_ang + sweep_ang)
def poly_arc(x, y, radius, start_ang, sweep_ang, num_points=2):
angle = sweep_ang / int(num_points)
a = start_ang
with beginShape():
while a <= start_ang + sweep_ang:
sx = x + cos(a) * radius
sy = y + sin(a) * radius
vertex(sx, sy)
a += angle
def arc_poly(x, y, d, _, start_ang, end_ang, num_points=5):
sweep_ang = end_ang - start_ang
angle = sweep_ang / int(num_points)
a = start_ang
with beginShape():
while a <= end_ang:
sx = x + cos(a) * d / 2
sy = y + sin(a) * d / 2
vertex(sx, sy)
a += angle
def bar(x1, y1, x2, y2, thickness=None, shorter=0, ends=(1, 1)):
"""
O código para fazer as barras, dois pares (x, y),
um parâmetro de encurtamento: shorter
"""
L = dist(x1, y1, x2, y2)
if not thickness:
thickness = 10
with pushMatrix():
translate(x1, y1)
angle = atan2(x1 - x2, y2 - y1)
rotate(angle)
offset = shorter / 2
line(thickness / 2, offset, thickness / 2, L - offset)
line(-thickness / 2, offset, -thickness / 2, L - offset)
if ends[0]:
half_circle(0, offset, thickness / 2, UP)
if ends[1]:
half_circle(0, L - offset, thickness / 2, DOWN)
def var_bar(p1x, p1y, p2x, p2y, r1, r2=None):
"""
Tangent/tangent shape on 2 circles of arbitrary radius
"""
if r2 is None:
r2 = r1
#line(p1x, p1y, p2x, p2y)
d = dist(p1x, p1y, p2x, p2y)
ri = r1 - r2
if d > abs(ri):
rid = (r1 - r2) / d
if rid > 1:
rid = 1
if rid < -1:
rid = -1
beta = asin(rid) + HALF_PI
with pushMatrix():
translate(p1x, p1y)
angle = atan2(p1x - p2x, p2y - p1y)
rotate(angle + HALF_PI)
x1 = cos(beta) * r1
y1 = sin(beta) * r1
x2 = cos(beta) * r2
y2 = sin(beta) * r2
#print((d, beta, ri, x1, y1, x2, y2))
beginShape()
b_arc(0, 0, r1 * 2, r1 * 2,
-beta - PI, beta - PI, mode=2)
b_arc(d, 0, r2 * 2, r2 * 2,
beta - PI, PI - beta, mode=2)
endShape(CLOSE)
else:
ellipse(p1x, p1y, r1 * 2, r1 * 2)
ellipse(p2x, p2y, r2 * 2, r2 * 2)
def b_arc(cx, cy, w, h, start_angle, end_angle, mode=0):
"""
A bezier approximation of an arc
using the same signature as the original Processing arc()
mode: 0 "normal" arc, using beginShape() and endShape()
1 "middle" used in recursive call of smaller arcs
2 "naked" like normal, but without beginShape() and endShape()
for use inside a larger PShape
"""
theta = end_angle - start_angle
# Compute raw Bezier coordinates.
if mode != 1 or abs(theta) < HALF_PI:
x0 = cos(theta / 2.0)
y0 = sin(theta / 2.0)
x3 = x0
y3 = 0 - y0
x1 = (4.0 - x0) / 3.0
if y0 != 0:
y1 = ((1.0 - x0) * (3.0 - x0)) / (3.0 * y0) # y0 != 0...
else:
y1 = 0
x2 = x1
y2 = 0 - y1
# Compute rotationally-offset Bezier coordinates, using:
# x' = cos(angle) * x - sin(angle) * y
# y' = sin(angle) * x + cos(angle) * y
bezAng = start_angle + theta / 2.0
cBezAng = cos(bezAng)
sBezAng = sin(bezAng)
rx0 = cBezAng * x0 - sBezAng * y0
ry0 = sBezAng * x0 + cBezAng * y0
rx1 = cBezAng * x1 - sBezAng * y1
ry1 = sBezAng * x1 + cBezAng * y1
rx2 = cBezAng * x2 - sBezAng * y2
ry2 = sBezAng * x2 + cBezAng * y2
rx3 = cBezAng * x3 - sBezAng * y3
ry3 = sBezAng * x3 + cBezAng * y3
# Compute scaled and translated Bezier coordinates.
rx, ry = w / 2.0, h / 2.0
px0 = cx + rx * rx0
py0 = cy + ry * ry0
px1 = cx + rx * rx1
py1 = cy + ry * ry1
px2 = cx + rx * rx2
py2 = cy + ry * ry2
px3 = cx + rx * rx3
py3 = cy + ry * ry3
# Debug points... comment this out!
# stroke(0)
# ellipse(px3, py3, 15, 15)
# ellipse(px0, py0, 5, 5)
# Drawing
if mode == 0: # 'normal' arc (not 'middle' nor 'naked')
beginShape()
if mode != 1: # if not 'middle'
vertex(px3, py3)
if abs(theta) < HALF_PI:
bezierVertex(px2, py2, px1, py1, px0, py0)
else:
# to avoid distortion, break into 2 smaller arcs
b_arc(cx, cy, w, h, start_angle, end_angle - theta / 2.0, mode=1)
b_arc(cx, cy, w, h, start_angle + theta / 2.0, end_angle, mode=1)
if mode == 0: # end of a 'normal' arc
endShape()