Concept definition

template<typename Shape>
concept geom::ProjectableObject =  DimensionalObject<Shape> and SdfObject<Shape> and
    requires (const Shape s, typename Shape::point_t p)
{
    { s.project(p) } -> std::convertible_to<typename Shape::point_t>;
    { s.normal(p)  } -> std::convertible_to<typename Shape::point_t>;
    { s.clip(p)    } -> std::convertible_to<typename Shape::point_t>;
}

Detailed Description

A shape which can perform an orthogonal projection to its boundary.

ProjectionObjects can also report their normal vectors— the direction away from the surface at any given point— and can implelement a clip(), which projects a point onto the surface if and only if it is outside.

ProjectionObject implies SdfObject, because the projection function can be used to implement the signed distance field.