Description:

superdeclarative geometry

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

If you get value from this package, please consider supporting SuperDeclarative!


Get Started #

dependencies:
superdeclarative_geometry: ^[VERSION]
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Quick Reference #
Angles #
Create an Angle from degrees or radians:
final degreesToRadians = Angle.fromDegrees(45);
final radiansToDegrees = Angle.fromRadians(pi / 4);
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Retrieve Angle values as degrees or radians:
myAngle.degrees;
myAngle.radians;
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Determine an Angle's direction and force it to be positive or negative:
myAngle.isPositive;
myAngle.isNegative;

myAngle.makePositive(); // Ex: -270° -> 90°
myAngle.makeNegative(); // Ex: 270° -> -90°
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Determine the category of an Angle:
myAngle.isAcute;
myAngle.isObtuse;
myAngle.isReflexive;
myAngle.category;
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Determine if two Angles are equivalent, regardless of direction:
Angle.fromDegrees(90).isEquivalentTo(Angle.fromDegrees(-270));
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Invert, add, subtract, multiply, and divide Angles:
-Angle.fromDegrees(30);

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

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

Angles.fromDegrees(45) * 2;

Angles.fromDegrees(90) / 2;
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Rotate an Angle:
final Rotation rotation = myAngle.rotate(Angle.fromDegrees(150));
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Rotations #
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);
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Add, subtract, multiply, and divide Rotations just like Angles.
Reduce a Rotation to an Angle:
Rotation.fromDegrees(540).reduceToAngle();
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Polar Coordinates #
Define polar coordinates by a radius and an angle, or by a Cartesian point:
PolarCoord(100, PolarCoord.fromDegrees(45));

CartesianPolarCoords.fromPoint(Point(0, 100));
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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;
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Map a PolarCoord to a Cartesian Point:
// Map to Cartesian coordinates.
final Point point = PolarCoord(100, Angle.fromDegrees(45)).toCartesian();
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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);
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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.

License

For personal and professional use. You cannot resell or redistribute these repositories in their original state.

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