Geometry Library

The Storm standard library provides a number of types for 2D and 3D geometry in its standard library. These are provided to make it easier for different graphics libraries to interact with each other, even if parts of them are implemented in C++.

All of these types and functions are in the core.geometry package. All their members treat the values as if they were immutable. That is, it is possible to modify the contents of all values except for Angle by assigning to their members. All member functions do, however, not modify the data structure, but instead return an updated copy. This typically makes it easier to chain operations conveniently without unintended side-effects.

Point

The value core.geometry.Point stores a 2-dimensional point expressed by 2 core.Floats named x and y. The implementation assumes that points appear in a coordinate system where positive x is towards the right, and positive y is downwards (as is typical for 2D computer graphics).

The Point type has the expected arithmetic operations as overloaded operators. Namely, addition, subtraction, multiplication with a scalar, and division by a scalar. The * operator for two points is overloaded as the dot product. It also has the following members:

The following free functions are also available:

Size

The value core.geometry.Size stores a 2-dimensional size expressed by 2 core.Floats named w and h (for width and height). Since the Size class is expected to represent a size, both of w and h are expected to be non-negative.

Overall, the size is convertible to a Point, and follows the same basic interface. However, due to the expectation that it contains a size, the interface is smaller. Apart from arithmetic operators, it has the following members:

Apart from the members, the following free functions are available:

Rect

The value core.geometry.Rect stores a 2-dimensional rectangle, expressed as two points, p0 and p1. The first point p0 is the top-left corner of the rectangle, and p1 is the bottom-right corner of the rectangle. The member functions of Rect considers the rectangle to contain all points from p0 up to, but not including p1. The class also contains the function size that computes the size of the rectangle. The size function also has an assignment variant, so it is possible to treat the point as if it cointained a point p0 for the top-left corner, and a size instead of two points.

The Rect type has overloads the + and - operators where the right hand side is a Point to translate a rectangle based on the coordinates in the point.

The Rect type has the following parameters:

The following free functions are also available:

Angle

The value core.geometry.Angle represents an angle in some unit (internally, radians is used, but this may change). The value overloads the operators + and - for adding and subtracting angles, and the operators * and / for multiplication and division by a scalar. While the Angle type does not contain any constructors, the functions deg and rad are provided instead. Furthermore, Basic Storm allows creating angles using units, like so: 

Angle a = 90 deg;
Angle b = 2.3 rad;
Float pi = (180 deg).rad();

An Angle is not limited to contain a value between 0 and 360 degrees. However, storing large angle values will yield a loss in precision. The member normalized normalizes the angle to between 0 and 360 degrees.

As mentioned above, the following functions are used to create angles from numbers in degrees or radians:

The Angle class contains the following members:

There are also a number of free functions that utilize angles together with other parts of the geometry package:

Vector

The library also provides a type for 3-dimensional coordinates. This type is name core.geometry.Vector. As with points, the type provides arithmetic operations for vector addition, subtraction, and multiplication with scalars. It is also possible to implicitly cast a Point into a Vector in order to make it easier to use transforms for both 2D and 3D coordinates.

The 3-dimensional Vector uses * for dot product, and / for cross product.

Apart from that, the interface is similar to that of Point, but some operations are missing due to them having a different meaning in 3 dimensions:

Similarly, there are also a few free functions:

Transform

The library also contains the core.geometry.Transform class, which represents a 3-dimensional affine transform using a 4 by 4 matrix. This means that the transform can represent arbitrary combinations of for example translation, rotation, scaling, skewing, and projections.

A transform interprets points or vectors as four-dimensional row-vectors. The fourth element, w, is set to 1 for the purposes of the transform. The row vector is multiplied with the transform matrix from the left, and the resulting four-dimensional vector is reduced to three dimensions by dividing the x, y, and z coordinates by w. As such, when transforms are multiplied together as a * b * c, then they will be applied from left to right with respect to the geometry.

The transform class itself has few members:

There are, however, a number of free functions that allow transforming points and vectors:

There are also a number of functions that create various transforms: