New Transformation API

[brendanzab]

Ok, so I have been experimting with a new transformation API. Here is one idea:

/// A type that can be interpreted as a geometric transformation.
pub trait Transformation: One + ScalarMul where
    Self::Scalar: BaseFloat,
{
    type Vector: InnerSpace<Scalar = Self::Scalar>;
    type Point: EuclideanSpace<Scalar = Self::Scalar, Diff = Self::Vector>;

    fn transform_vector(&self, vector: Self::Vector) -> Self::Vector;
    fn transform_point(&self, point: Self::Point) -> Self::Point;
}

/// A transformation that can apply a translation.
pub trait Translation: Transformation where
    Self::Scalar: BaseFloat,
{
    fn from_translation(translation: Self::Vector) -> Self;
}

/// A transformation that can apply a uniform scale factor.
pub trait UniformScale: Transformation where
    Self::Scalar: BaseFloat,
{
    fn from_scale(factor: Self::Scalar) -> Self;
}

/// A transformation that can apply a scale factor that is different in each
/// dimension.
pub trait NonUniformScale: UniformScale where
    Self::Scalar: BaseFloat,
{
    fn from_non_uniform_scale(scale: Self::Vector) -> Self;
}

/// A transformation that can apply a rotation.
pub trait Rotation: Transformation where
    Self::Scalar: BaseFloat,
{
    type Angle: Angle<Unitless = Self::Scalar>;
}

/// A transformation that can apply a rotation in 2-dimensional space.
pub trait Rotation2d: Rotation where
    Self::Scalar: BaseFloat,
    Self: From<<Self as Rotation>::Angle>,
{}

/// A transformation that can apply a rotation in 3-dimensional space.
pub trait Rotation3d: Rotation where
    Self::Scalar: BaseFloat,
    Self: From<Euler<<Self as Rotation>::Angle>>,
{
    fn from_axis_angle(axis: Self::Vector, angle: Self::Angle) -> Self;
    fn from_angle_x(theta: Self::Angle) -> Self;
    fn from_angle_y(theta: Self::Angle) -> Self;
    fn from_angle_z(theta: Self::Angle) -> Self;
}

Thoughts? Any ideas for improvements?

Still need to figure out how inversion fits into this...

cc. #347 #337

[kvark]

You can have a default implementation for transform_vector, based on the transform_point one.

I don't think that building traits on top just to have more constructors is an elegant solution. Imagine, how many traits would the old Decomposed struct need to implement - Transform, Translation, Scale, NonUniformScale, Rotation, Rotation3d, maybe more.

[brendanzab]

Yeah, I'm not sure - just playing around still. :/