UV coordinates within plane

[ppizarror]

Hi! I need the (U, V) coordinates given a (X, Y, Z) coplanar to a plane p, for example, for plane defined in:

acme::point pA(5.02339, -0.81223, -1.13819); // Origin
acme::point pB(2.32428, 2.78375, 1.50523);
acme::point pC(-0.29562, -0.53994, 2.78661);
acme::triangle t(pA, pB, pC);
acme::plane p(pA, t.normal());

And taking as basis e1, e2:

acme::vec3 n = p.normal();
acme::vec3 e1 = n.cross(acme::vec3(1, 0, 0)).normalized();
if (e1.isZero()) e1 = n.cross(acme::vec3(0, 0, 1)).normalized();
acme::vec3 e2 = n.cross(e1).normalized();

Computing UV for any coordinate is relatively easy, by computing the dot product of the base and the relative distance of any point to the origin of the plane. For example, for point point:

acme::point pointRelative = point - p.origin();
acme::vec2 pointUV(e1.dot(pointRelative), e2.dot(pointRelative));

The question is, can we add this feature to the plane object? It is desirable in acme? All previous steps can be resumed on a single function

p.getUV(acme::point);
p.fromUV(acme::vec2);

Examples:

acme::point xyz(1.10808, -2.2061, 1.45032);
acme::vec2 uv = p.getUV(xyz); // [ -8.902579e-01, 4.814598e+00 ]'
acme::point p =p.fromUV(uv); // p == xyz

• Why this is important or needed? Well... I need to triangulate coplanar points in 3D. Thus, using their UV representation is much simpler as algorithms like constrained Delaunay/Voronoi are simple to implement... also allows for reducing dimensionality and performing other planar algorithms.

Greetings!

[StoccoDavide]

Hi! acme has been initially thought only for strictly 3D geometrical operations but I can add the feature you requested.

If you need 2D support, you have good ideas on how to support mixed 2/3D operations, and you want to contribute to the repo, we can think about adding together the 2D section to acme.

Greetings!

[ppizarror]

I think you are right... maybe we can address that in the future, I'll close this for now as the main goal must be a complete 3D Framework. Thanks!