SuperDeclarative Geometry

First-class support for angles, polar coordinates, and related math.

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  superdeclarative_geometry: ^[VERSION]

Quick Reference


Create an Angle from degrees or radians:

final degreesToRadians = Angle.fromDegrees(45);
final radiansToDegrees = Angle.fromRadians(pi / 4);

Retrieve Angle values as degrees or radians:


Determine an Angle's direction and force it to be positive or negative:


myAngle.makePositive(); // Ex: -270° ->  90°
myAngle.makeNegative(); // Ex:  270° -> -90°

Determine the category of an Angle:


Determine if two Angles are equivalent, regardless of direction:


Invert, add, subtract, multiply, and divide Angles:


Angle.fromDegrees(30) + Angle.fromDegrees(15);

Angle.fromDegrees(30) - Angle.fromDegrees(15);

Angles.fromDegrees(45) * 2;

Angles.fromDegrees(90) / 2;

Rotate an Angle:

final Rotation rotation = myAngle.rotate(Angle.fromDegrees(150));


Angles are confined to values in (-360°, 360°). For values beyond this range, the concept of a Rotation is provided.

A Rotation is almost identical to an Angle except that a Rotation can be arbitrarily large in the positive or negative direction. This allows for the accumulation of turns over time.

Create a Rotation:

final rotation = Rotation.fromDegrees(540);

Add, subtract, multiply, and divide Rotations just like Angles.

Reduce a Rotation to an Angle:


Polar Coordinates

Define polar coordinates by a radius and an angle, or by a Cartesian point:

PolarCoord(100, PolarCoord.fromDegrees(45));

PolarCoord.fromCartesian(0, 100);

Add, subtract, multiply, and divide PolarCoords:

PolarCoord(100, Angle.fromDegrees(45)) + PolarCoord(200, Angle.fromDegrees(135));

PolarCoord(100, Angle.fromDegrees(45)) - PolarCoord(200, Angle.fromDegrees(135));

PolarCoord(100, Angle.fromDegrees(15)) * 2;

PolarCoord(200, Angle.fromDegrees(30)) / 2;

Map a PolarCoord to a Cartesian Point:

// Map to Cartesian coordinates.
final Point point = PolarCoord(100, Angle.fromDegrees(45)).toCartesian();

Cartesian Orientations

Different use-cases treat angles in different ways.

Mathematics treats the positive x-axis as a 0° angle and treats positive angles as running counter-clockwise.

Flutter app screens treat the positive x-axis as a 0° angle, but then treats positive angles as running clockwise.

Ship navigation treats the positive y-axis as a 0° angle and then treats positive angles as running clockwise.

Each of these situations apply a different orientation when mapping an angle, or a polar coordinate, to a location in Cartesian space. This concept of orientation is supported by superdeclarative_geometry by way of CartesianOrientations.

Both Angle and PolarCoord support CartesianOrientation mappings.

final polarCoord = PolarCoord(100, Angle.fromDegrees(30));

// Treat angles like a Flutter screen.
// This point is 30° clockwise from the x-axis.
final screenPoint = polarCoord.toCartesian(); // defaults to "screen" orientation

// Treat angles like mathematics.
// This point is 30° counter-clockwise from the x-axis.
final mathPoint = polarCoord.toCartesian(orientation: CartesianOrientation.math);

// Treat angles like navigators.
// This point is 30° clockwise from the y-axis.
final navigationPoint = polarCoord.toCartesian(orientation: CartesianOrientation.navigation);

You can define a custom CartesianOrientation by implementing the interface. Then, you can pass an instance of your custom orientation into PolarCoord's toCartesian() method.