2D 和 3D 向量的正确类层次结构 [英] proper class hierarchy for 2D and 3D vectors

问题描述

我想要一个通用的向量抽象类/特征来指定某些方法，例如:

I want to have a general vector abstract class / trait that specifies certain methods, e.g.:

trait Vec 
{
  def +(v:Vec):Vec
  def *(d:Double):Vec

  def dot(v:Vec):Double
  def norm:Double
}

我想让 Vec2D 和 Vec3D 扩展 Vec:

I want to have Vec2D and Vec3D extend Vec:

class Vec2D extends Vec { /* implementation */ }
class Vec3D extends Vec { /* implementation */ }

但是，例如，我如何才能使 Vec2D 只能添加到其他 Vec2D 而不能添加到 Vec3D?

But how can I, for instance, make it so that Vec2D can only be added to other Vec2D and not to Vec3D?

现在我只是在没有共同的 Vec 祖先的情况下实现 Vec2D 和 Vec3D，但这会因重复代码而变得乏味.我必须实现所有依赖于这些类的几何类(例如 Triangle、Polygon、Mesh、...)两次，一次用于Vec2D 和 Vec3D.

Right now I'm just implementing Vec2D and Vec3D without a common Vec ancestor, but this is getting tedious with duplicate code. I have to implement all my geometry classes that depend on these classes (e.g. Triangle, Polygon, Mesh, ...) twice, once for Vec2D and again for Vec3D.

我看到 java 实现:javax.vecmath.Vector2d 和 javax.vecmath.Vector3d 没有共同的祖先.这是什么原因?有没有办法在 Scala 中克服它?

I see the java implementations: javax.vecmath.Vector2d and javax.vecmath.Vector3d do not have a common ancestor. What's the reason for this? Is there a way to overcome it in scala?

推荐答案

As requested，设计基本特征的最有用方法包括 CRTP 和 自类型注释.

As requested, the most useful way of designing the base trait involves both the CRTP and the self-type annotation.

trait Vec[T <: Vec[T]] { this: T =>
  def -(v: T): T
  def *(d: Double): T

  def dot(v: T): Double
  def norm: Double = math.sqrt(this dot this)
  def dist(v: T) = (this - v).norm
}

如果没有self类型，就不可能调用this.dot(this)，因为dot需要一个T；因此我们需要通过注解来强制执行.

Without the self-type, it is not possible to call this.dot(this) as dot expects a T; therefore we need to enforce it with the annotation.

另一方面，如果没有 CRTP，我们将无法在 (this - v) 上调用 norm，因为 - 返回一个 T 因此我们需要确保我们的类型 T 有这个方法，例如声明T 是一个 Vec[T].

On the other hand, without CRTP, we’ll fail to call norm on (this - v) as - returns a T and thus we need to make sure that our type T has this method, e.g. declare that T is a Vec[T].

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