Points and Interpolations

Input Amount: Trade size in atoms
Price Factor: Adjustment relative to mid-price - equivalent to spread
Interpolation Mode: How pricing transitions to the next point

Overview

Points and interpolations are the means by which you define curves.

Each bid or ask curve consists of control points. Every point specifies:

Points define the shape of the curve; interpolation determines the behavior between them.

Hadron supports multiple interpolation types, which can be mixed across points:

Step (0): Constant price factor between point A → B.
Linear (1): Linearly interpolates price between points.
Marginal Step (2): Points store average spread, producing constant marginal pricing between A → B. Gives orderbook-like behavior where each size tier has a flat marginal price.
Hyperbolic (3): Rational easing with shape parameter k .
k=1.0 is exactly linear, k<1.0 is concave (saturating), k>1.0 is convex (accelerating).
Quadratic (4): Quadratic easing with shape parameter k. Formula: ease(t) = t + k*(t² - t). k=0 is linear, k>0 is convex (stays near f0 longer), k<0 is concave (moves toward f1 quickly).
Cubic (5): Cubic easing with 2 shape parameters a and b. Formula: ease(t) = t + a*(t² - t) + b*(t³ - t). a=0,b=0 is linear. Allows S-curves and richer shapes.

By combining points and interpolation types, makers can construct virtually any curve shape — from order-book ladders to smooth nonlinear depths.

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