CubicBezier
CubicBezier(a, b, c, d)
Located in ursina/curve.py
Overview
CubicBezier implements a cubic Bézier easing function defined by four control points (0,0), (a,b), (c,d), (1,1). Use it whenever you need a custom easing curve in Entity.animate_* calls.
Properties
| Name | Description |
|---|---|
.a | X coordinate of first control point |
.b | Y coordinate of first control point |
.c | X coordinate of second control point |
.d | Y coordinate of second control point |
.ax | Precomputed coefficient for t³ term in X polynomial |
.bx | Precomputed coefficient for t² term in X polynomial |
.cx | Precomputed coefficient for t¹ term in X polynomial |
.ay | Precomputed coefficient for t³ term in Y polynomial |
.by | Precomputed coefficient for t² term in Y polynomial |
.cy | Precomputed coefficient for t¹ term in Y polynomial |
Methods
| Method | Description |
|---|---|
sample_curve_x(t) | Return the X value of the Bézier at parameter t. |
sample_curve_y(t) | Return the Y value of the Bézier at parameter t. |
sample_curve_derivative_x(t) | Return the derivative dX/dt at parameter t. |
solve_curve_x(t, epsilon) | Numerically solve for parameter t that yields sample_curve_x(t) ≈ x. |
calculate(x, epsilon) | Given an input progress x (0–1), return the eased output by solving inverse X. |
Example
from ursina import *
from ursina.curve import CubicBezier, combine, linear, reverse, in_expo
app = Ursina()
camera.orthographic = True
camera.fov = 16
window.color = color.black
# render the curve as a line
def render_curve(fn, name):
verts = [Vec3(i/31, fn(i/31), 0) for i in range(32)]
c = Entity(model=Mesh(vertices=verts, mode='line', thickness=2), color=color.light_gray)
Text(parent=c, text=name, scale=8, color=color.gray, y=-0.1)
return c
# simple Bézier: start slow, speed up, slow again
bez = CubicBezier(0, .5, 1, .5)
print('Value at x=0.23 →', bez.calculate(.23))
# combine two curves for a custom effect
custom = combine(linear, reverse(in_expo), 0.25)
render_curve(custom, 'custom_combine')
# Bézier example in animation
e = Entity(model='cube')
e.animate_y(2, duration=1, curve=bez)
EditorCamera()
app.run()