UrsinaMath

A collection of standalone functions for common math tasks in 2D/3D space, color interpolation, clamping, and array utilities.

Functions

Function	Description
`distance(a, b)`	Full 3D distance between points or entities.
`distance_2d(a, b)`	Distance in the X–Y plane.
`distance_xz(a, b)`	Distance in the X–Z plane.
`lerp(a, b, t)`	Linear interpolation between `a` and `b` at `t` (0–1). Supports numbers, tuples, Vec2, Vec3, lists.
`inverselerp(a, b, t)`	Given `t` between `a` and `b`, return the normalized position (0–1).
`lerp_angle(start_angle, end_angle, t)`	Interpolate angles correctly across the 360° boundary.
`slerp(q1, q2, t)`	Spherical linear interpolation between two quaternions.
`clamp(value, floor, ceiling)`	Constrain a value to the given range.
`round_to_closest(value, step=0)`	Round to the nearest multiple of `step`. If `step=0`, behaves like `round()`.
`rotate_around_point_2d(point, origin, deg)`	Rotate a 2D point around an origin by `deg` degrees.
`world_position_to_screen_position(point)`	Convert a world-space `Vec3` to UI-space `(x,y)`.
`sum(l)`	Sum all elements in an iterable.
`make_gradient(index_color_dict)`	Given `{index: color}`, return a 256-entry list smoothly interpolated between colors.
`sample_gradient(list_of_values, t)`	Distribute `list_of_values` evenly along 0–1 and return the interpolated entry at `t`.

Example

from ursina import *
from ursina.ursinamath import *

app = Ursina()

# distance examples
e1 = Entity(position=(0,0,0))
e2 = Entity(position=(0,1,1))
print(distance(e1, e2))           # full 3D distance
print(distance_xz(e1, e2.position))  # XZ-plane only

# interpolation examples
between_color = lerp(color.lime, color.magenta, .5)
print(between_color)

print(lerp((0,0), (0,1), .5))
print(lerp(Vec2(0,0), Vec2(0,1), .5))
print(lerp([0,0], [0,1], .5))

# angle rotation
p = (1,0)
print(p, 'rotated ->', rotate_around_point_2d(p, (0,0), 90))

app.run()