ear clipping using pnpoly algorithm - #156

Super cool! Merged!

@raspofabs We found a bug that internal angle test in trinangulation fails in some case: https://github.com/tinyobjloader/tinyobjloader/issues/295

The situation is

• (signed) area is calculated over the polygon
• the signedness of area become wrong depending on the value of vertex coordinate
• each angle is falsely detected as internal angle(even for the square polygon)
• remainingFace.vertex_indices.size() become 4 or more, resulting some faces become disappear.

  tinyobjloader/tiny_obj_loader.h

  Line 1575 in 9173980

  if (remainingFace.vertex_indices.size() == 3) {

Computing signed area per triangle seems correctly handle internal angle test. Code is somewhat like this:

            real_t e0x = vx[1] - vx[0];
            real_t e0y = vy[1] - vy[0];
            real_t e1x = vx[2] - vx[1];
            real_t e1y = vy[2] - vy[1];
            real_t cross = e0x * e1y - e0y * e1x;

            real_t area = (vx[0] * vy[1] - vy[0] * vx[1]) * static_cast<real_t>(0.5);

            // if an internal angle
            if (cross * area < static_cast<real_t>(0.0)) {
              guess_vert += 1;
              continue;
            }

@raspofabs Do you think this is the correct solution?

@raspofabs We found a bug that internal angle test in trinangulation fails in some case: #295

The situation is

* (signed) `area` is calculated over the polygon

* the signedness of `area` become wrong depending on the value of vertex coordinate

* each angle is falsely detected as internal angle(even for the square polygon)

* `remainingFace.vertex_indices.size()` become 4 or more, resulting some faces become disappear. https://github.com/tinyobjloader/tinyobjloader/blob/9173980d1de273b17eba5e10eb189e8b4be89425/tiny_obj_loader.h#L1575

Computing signed area per triangle seems correctly handle internal angle test. Code is somewhat like this:

            real_t e0x = vx[1] - vx[0];
            real_t e0y = vy[1] - vy[0];
            real_t e1x = vx[2] - vx[1];
            real_t e1y = vy[2] - vy[1];
            real_t cross = e0x * e1y - e0y * e1x;

            real_t area = (vx[0] * vy[1] - vy[0] * vx[1]) * static_cast<real_t>(0.5);

            // if an internal angle
            if (cross * area < static_cast<real_t>(0.0)) {
              guess_vert += 1;
              continue;
            }

@raspofabs Do you think this is the correct solution?

Sorry, my mistake. Yes, it looks like the problem is precision during the area calculation.
A simple fix (imo) would be to subtract the first coordinate from every vertex position before committing to doing the calculations. Then there will always be a vertex at 0,0,0 and the likelihood of precision issues occuring should be vastly reduced.

so, take a vertex at random (first is fine), then subtract that vertex's values from all others before doing analysis of the vertices. I can't work on this at the moment as I don't have a machine set up for development right now.

@raspofabs Thanks!

A simple fix (imo) would be to subtract the first coordinate from every vertex position before committing to doing the calculations. Then there will always be a vertex at 0,0,0 and the likelihood of precision issues occuring should be vastly reduced.

I see. So compute area over polygon(not per trinagle) based on relative vertex coordinate(e.g. move the first vertex to the origin) would solve the issue. I will try it to implement.

BTW I have integrated mapbox's earcut into tinyobjloader. We can verify the correctness with it: #298

@raspofabs After reading algorithm description of earcut, area is calculated per face, not over the polygon. Precision wasn't a problem.