calendis / magician

Math engine

Magician

Magician is in extremely early stages and is a general-purpose mathematical engine for generating and visualizing data, built with a simple API in mind.

Features/Design

Magician is built around two core abstractions, Multis and Maps.

Multi

A Multi is a tree of 3-vectors that defines geometrical objects

Each Multi stores its position relative to its parent in the tree. A Multi contains flags that determine how it is drawn, either as a plot, or a 2D/3D geometrical shape.

Maps

Maps represent mathematical functions from some number of inputs to some number of outputs

RelationalMap

The most general case, a relational map allows for any number of ins to any number of outs

InverseParamMap

An IPM allows for any number of ins, but only one out. This is a solved equation, a function t = f(x,y,z,...)

ParamMap

A ParamMap allows for any number of outs, but only one in. This is a parametric equation f(t) = (x,y,z,...)

DirectMap

A DirectMap allowed for zero or one ins, and exactly one out. This is a function of a single variable y = f(x)

Interactivity

Magician currently offers limited user interactivity. Controls and Sensors defineable through Maps

Usage/Examples

Currently, Magician has basic functionality, but is not ready for general use. It is best used by writing a class that inherits Spell, loading it with the Spellcaster, and calling the Spell methods from the SDL loop. A spell consists of the Preloop, which runs once and the Loop, which runs every frame. The following examples are written in the Preloop.

These examples reflect usage as of Magician Alpha 0.0, and may break at any time

// Create an equilateral triangle with radius 60 in the upper-right quadrant
Origin["myTriangle"] = RegularPolygon(100, 100, 3, 60);

// Create a pentagon with radius 100, with a random easy-to-see colour
Origin["myPentagon"] = RegularPolygon(5, 100).Colored(
    HSLA.Random(saturation: 1, lightness: 1, alpha: 120)
);

...
// Let that pentagon track the mouse cursor
Origin["myPentagon"].DrivenXY(
    x => Events.MouseX,
    y => Events.MouseY
);

...
// Now let that pentagon revolve about the origin, while still tracking the mouse
Origin["myPentagon"].DrivenPM(
    p => Data.Env.Time,
    m => m
);

...
// Let that pentagon rotate about its axis
Origin["myPentagon"].Sub(m => m
    .DrivenPM(
        p => p + 0.1,
        m => m
    )
);

Origin["parametric"] = new Multimap(1,
    x => 180 * Math.Cos(x / 3),
    y => 180 * Math.Sin(y / 7)
).TextAlong(-49, 49, 0.3, "Here's an example of a Multimap with 1 input and two outputs being used to draw text parametrically",
new RGBA(0x00ff9080));

Acknowledgements

Thanks to these people for sharing their knowledge.

• Atul Narkhede, Dinesh Manocha
• Yuvraj Nigade, Pushkar Newaskar
• Lazyfoo

Gallery

Some cool screenshots