12. Useful maths

funground adds a few helpers that come up all the time in drawing. For everything else — sqrt, sin, cos, atan2, pi, floor — use Python's own math module (import math). Remember that f.rotate() takes degrees while math.sin wants radians: convert with f.radians() and f.degrees().

Helper	What it gives	Example
f.map_range(v, a1, b1, a2, b2)	v re-scaled from the range a1..b1 to a2..b2	f.map_range(f.mouse_x, 0, f.width, 0, 255)
f.map_range(..., clamp=True)	the same, kept inside a2..b2
f.lerp(a, b, t)	the number t of the way from a to b (0 → a, 1 → b)	f.lerp(0, 100, 0.25) is 25
f.norm(v, a, b)	where v sits between a and b, as 0 to 1	f.norm(15, 10, 20) is 0.5
f.mag(x, y)	the length of the arrow (x, y)	f.mag(3, 4) is 5
f.constrain(v, low, high)	v, kept between low and high
f.distance(x1, y1, x2, y2)	how far apart two points are

(It is called map_range, not map, so it never hides Python's own map.)

import funground as f


def setup():
    f.size(640, 200)


def draw():
    f.background("white")
    f.no_stroke()
    for i in range(12):
        x = f.map_range(i, 0, 11, 40, 600)
        shade = f.map_range(i, 0, 11, 230, 30)
        f.fill((shade, shade, 255))
        f.circle(x, 100, 40)


f.run()

Vectors

A vector keeps an x and a y together: a position, a speed, a push. f.Vector(3, 4) is an arrow 3 across and 4 down; v.x and v.y are its parts, and v.mag() is its length, 5.

Moving things is then two lines: forces add to the velocity, the velocity adds to the position.

Call	Does	Note
v.add(w), v.sub(w)	adds or subtracts w	changes v
v.mult(n), v.div(n)	scales by n	changes v
v.limit(n), v.set_mag(n)	caps or sets the length	changes v
v.normalize()	makes the length 1	changes v
v.rotate(degrees)	turns it	changes v
v.mag(), v.heading()	length; direction in degrees (0 = right, 90 = down)	a number
v.dist(w), v.dot(w)	distance to w; dot product	a number
v + w, v * 2	a new vector	v unchanged
f.Vector.from_angle(degrees, length)	a vector pointing that way	new

Methods such as add change the vector itself, as in p5.js, so position.add(velocity) moves the position. Use copy() when you want to keep the original, or write position + velocity.

import funground as f

position = f.Vector(40, 100)
velocity = f.Vector(3, -4)
gravity = f.Vector(0, 0.2)


def setup():
    f.size(640, 200)


def draw():
    f.background("white")
    velocity.add(gravity)
    position.add(velocity)
    if position.y > 180:
        velocity.y *= -0.8
        position.y = 180
    f.fill("tomato")
    f.circle(position.x, position.y, 30)


f.run()

See also

• Gallery: Useful maths and Motion.
• Quick Reference: 5. Mouse, keyboard and useful helpers.
• Words: vector.

Try it

1. Use f.map_range() to turn the mouse's x into a colour from 0 to 255.
2. Draw 10 circles between two points with f.lerp(), spaced evenly.
3. Make a ball with a f.Vector position and speed that bounces off all four edges.

Next: 13. Saving your work