Curves

Introduction

Curves aims to be the best elixir framework for calculating bezier curves and splines.

curve = Curves.define_bezier(:ease_out)
{x, y} = Curves.solve!(curve, 0.25)
assert is_float(x)
assert is_float(y)

Directory

Be sure to check out the livebook for an interactive demo/tutorial.

• Hex docs
• Hex package
• Github Repo

Visual Demo

Ease in-out Bezier

The simplest way to use Curves is with the predefined ones like :ease_in_out

curves = Curves.define_bezier(:ease_in_out)
for i <- 0..1000 do
  Curves.solve!(curve, i / 1000)
end
|> # render_vega_lite_chart(...)

Quadratic Bezier

Here we make an asymmetric quadratic curve

points = [
  {0, 0},
  {20, 50},
  {100, 0}
]
curves = Curves.define_bezier(points)

Custom 4-point Bezier

points = [
  {0, 0},
  {0.8, 0.2},
  {0.3, 2.2},
  {1, 1}
]
curves = Curves.define_bezier(points)

Spline examples

The simplest spline is basically just a series of bezier curves connected to each other. Notice we are no longer using define_bezier, but define_bezier_spline. Now it is a list of lists with 1, 2, or 3 tuples in each segment.

# points format for `define_bezier_spline/2`
[{knot_x, knot_y}]
[{knot_x, knot_y}, {cp0_x, cp0_y}]
[{knot_x, knot_y}, {cp0_x, cp0_y}, {cp1_x, cp1_y}]

Bezier Spline

points = [
  # P0
  [{5.0, 10.0},  # Knot
  {10.0, 10.0}], # control point 0

  # P1
  [{10.0, 5.0},  # Knot
    {5.0, 5.0},  # control point 0
    {15.0, 5.0}],# control point 1

  # P2
  [{15.0, 10.0}, # Knot
   {15.0, 6.0},  # control point 0
   {15.0, 14.0}  # control point 1
  ],

  # P3
  [{20.0, 15.0}, # Knot
   {18.0, 15.0}, # control point 0
   {23.0, 15.0}],# control point 1

  # P4
  [{30.0, 10.0}, # Knot
    {32.0, 5.0}] # control point 0
]
curves = Curves.define_bezier_spline(points)

Cubic Hermite Spline

Sometimes we don't want to manually define every control point. The Hermite spline automatically calculates it based on the first derivative at the start and end point of each segment.

curve = Curves.define_hermite([
  {5, 10},
  {10, 5},
  {15, 10},
  {20, 10},
  {25, 5},
  {30, 15},
])

Catmull-Rom Spline

Similar to the Hermite spline, but now the derivative comes from the slope between the previous and next point.

curve = Curves.define_catmull_rom([
  {0, 0},
  {1, 0},
  {1, 1},
  {0, 1},
  {0, 2},
  {1, 2},
])

B-Spline

The smoothest of the splines featured here, but with the drawback that the line does not actually pass through the control points.

curve = Curves.define_b_spline([
    {0, -2},
    {3, 4},
    {6, 5},
    {7, -1},
    {10, 3},
    {5, 1},
    {12, 9}
])