Depth and Smooth Fits

Depth and Smooth Fits

Your two questions, tested. Shading is only useful if it changes the shape, so here it becomes depth: how far the surface is from the camera at each pixel, and everything in front of it is carved away. And the fitted tubes are meshed smoothly instead of in steps.

  • Exact depth is the biggest gain so far. With the six straight views, part overlap with the true model rises by 0.10 to 0.24 on every model; the anglerfish's mouth goes from 75% filled to 56%, and with all 26 views from 73% to 23%. It cuts away nothing of the true shape (up to 2.4% on the jellyfish, whose tentacles are thinner than a grid cell).
  • Depth worked out from surface direction alone, as I built it, does not work. The overlap rises in only 5 of 24 cases, and on the octopus and scorpion it cuts away up to 37% of the true shape: where one arm lies over another, the depth jumps, and surface direction cannot show a jump. Depth has to come from something that sees jumps.
  • The steps were in the meshing, not the fit. Re-meshed from the same fitted tubes, the arms are smooth. Scores barely move, except the jellyfish's thin tentacles, which the steps had broken up.
  • AI pictures: right side and underside drawn and painted for all seven; special angles for four (three wait on a redraw after a bug of mine); fits running on the lab.

1. Carving by depth: does the shape get closer to the true one?

The true models again, with three view sets. Each shape is carved from the outlines first, then further with each view's depth: the exact depth from the true model (the most depth could do), and depth worked out only from the surface direction, which is what shading tells (exact, then off by 10° and 20°, as an estimator reading AI pictures would be).

outlines onlyoutlines onlyexact depthexact depthdepth from surface directiondepth from surface directionthe same, direction off by 10°the same, direction off by 10°the same, direction off by 20°the same, direction off by 20°
0.30.40.50.60.70.80.91.0Flamingo6 straight viewsFlamingo, 6 straight views, outlines only: 0.694Flamingo, 6 straight views, exact depth: 0.793Flamingo, 6 straight views, depth from surface direction: 0.696Flamingo, 6 straight views, the same, direction off by 10°: 0.696Flamingo, 6 straight views, the same, direction off by 20°: 0.6966 + 4 special anglesFlamingo, 6 + 4 special angles, outlines only: 0.834Flamingo, 6 + 4 special angles, exact depth: 0.857Flamingo, 6 + 4 special angles, depth from surface direction: 0.835Flamingo, 6 + 4 special angles, the same, direction off by 10°: 0.836Flamingo, 6 + 4 special angles, the same, direction off by 20°: 0.833all 26 viewsFlamingo, all 26 views, outlines only: 0.871Flamingo, all 26 views, exact depth: 0.884Flamingo, all 26 views, depth from surface direction: 0.866Flamingo, all 26 views, the same, direction off by 10°: 0.858Flamingo, all 26 views, the same, direction off by 20°: 0.869Agama6 straight viewsAgama, 6 straight views, outlines only: 0.582Agama, 6 straight views, exact depth: 0.685Agama, 6 straight views, depth from surface direction: 0.585Agama, 6 straight views, the same, direction off by 10°: 0.585Agama, 6 straight views, the same, direction off by 20°: 0.5866 + 4 special anglesAgama, 6 + 4 special angles, outlines only: 0.755Agama, 6 + 4 special angles, exact depth: 0.780Agama, 6 + 4 special angles, depth from surface direction: 0.759Agama, 6 + 4 special angles, the same, direction off by 10°: 0.758Agama, 6 + 4 special angles, the same, direction off by 20°: 0.757all 26 viewsAgama, all 26 views, outlines only: 0.831Agama, all 26 views, exact depth: 0.836Agama, all 26 views, depth from surface direction: 0.831Agama, all 26 views, the same, direction off by 10°: 0.817Agama, all 26 views, the same, direction off by 20°: 0.815Scorpion6 straight viewsScorpion, 6 straight views, outlines only: 0.336Scorpion, 6 straight views, exact depth: 0.533Scorpion, 6 straight views, depth from surface direction: 0.338Scorpion, 6 straight views, the same, direction off by 10°: 0.338Scorpion, 6 straight views, the same, direction off by 20°: 0.3396 + 4 special anglesScorpion, 6 + 4 special angles, outlines only: 0.499Scorpion, 6 + 4 special angles, exact depth: 0.605Scorpion, 6 + 4 special angles, depth from surface direction: 0.450Scorpion, 6 + 4 special angles, the same, direction off by 10°: 0.457Scorpion, 6 + 4 special angles, the same, direction off by 20°: 0.469all 26 viewsScorpion, all 26 views, outlines only: 0.590Scorpion, all 26 views, exact depth: 0.659Scorpion, all 26 views, depth from surface direction: 0.438Scorpion, all 26 views, the same, direction off by 10°: 0.437Scorpion, all 26 views, the same, direction off by 20°: 0.435Octopus6 straight viewsOctopus, 6 straight views, outlines only: 0.617Octopus, 6 straight views, exact depth: 0.861Octopus, 6 straight views, depth from surface direction: 0.619Octopus, 6 straight views, the same, direction off by 10°: 0.620Octopus, 6 straight views, the same, direction off by 20°: 0.6206 + 4 special anglesOctopus, 6 + 4 special angles, outlines only: 0.779Octopus, 6 + 4 special angles, exact depth: 0.900Octopus, 6 + 4 special angles, depth from surface direction: 0.743Octopus, 6 + 4 special angles, the same, direction off by 10°: 0.754Octopus, 6 + 4 special angles, the same, direction off by 20°: 0.750all 26 viewsOctopus, all 26 views, outlines only: 0.853Octopus, all 26 views, exact depth: 0.929Octopus, all 26 views, depth from surface direction: 0.734Octopus, all 26 views, the same, direction off by 10°: 0.705Octopus, all 26 views, the same, direction off by 20°: 0.683Seahorse6 straight viewsSeahorse, 6 straight views, outlines only: 0.708Seahorse, 6 straight views, exact depth: 0.808Seahorse, 6 straight views, depth from surface direction: 0.701Seahorse, 6 straight views, the same, direction off by 10°: 0.702Seahorse, 6 straight views, the same, direction off by 20°: 0.7026 + 4 special anglesSeahorse, 6 + 4 special angles, outlines only: 0.809Seahorse, 6 + 4 special angles, exact depth: 0.852Seahorse, 6 + 4 special angles, depth from surface direction: 0.784Seahorse, 6 + 4 special angles, the same, direction off by 10°: 0.774Seahorse, 6 + 4 special angles, the same, direction off by 20°: 0.788all 26 viewsSeahorse, all 26 views, outlines only: 0.843Seahorse, all 26 views, exact depth: 0.875Seahorse, all 26 views, depth from surface direction: 0.809Seahorse, all 26 views, the same, direction off by 10°: 0.791Seahorse, all 26 views, the same, direction off by 20°: 0.809Racer snake6 straight viewsRacer snake, 6 straight views, outlines only: 0.631Racer snake, 6 straight views, exact depth: 0.727Racer snake, 6 straight views, depth from surface direction: 0.635Racer snake, 6 straight views, the same, direction off by 10°: 0.635Racer snake, 6 straight views, the same, direction off by 20°: 0.6346 + 4 special anglesRacer snake, 6 + 4 special angles, outlines only: 0.783Racer snake, 6 + 4 special angles, exact depth: 0.816Racer snake, 6 + 4 special angles, depth from surface direction: 0.787Racer snake, 6 + 4 special angles, the same, direction off by 10°: 0.786Racer snake, 6 + 4 special angles, the same, direction off by 20°: 0.777all 26 viewsRacer snake, all 26 views, outlines only: 0.815Racer snake, all 26 views, exact depth: 0.831Racer snake, all 26 views, depth from surface direction: 0.817Racer snake, all 26 views, the same, direction off by 10°: 0.812Racer snake, all 26 views, the same, direction off by 20°: 0.765Jellyfish6 straight viewsJellyfish, 6 straight views, outlines only: 0.350Jellyfish, 6 straight views, exact depth: 0.444Jellyfish, 6 straight views, depth from surface direction: 0.350Jellyfish, 6 straight views, the same, direction off by 10°: 0.350Jellyfish, 6 straight views, the same, direction off by 20°: 0.3516 + 4 special anglesJellyfish, 6 + 4 special angles, outlines only: 0.387Jellyfish, 6 + 4 special angles, exact depth: 0.506Jellyfish, 6 + 4 special angles, depth from surface direction: 0.409Jellyfish, 6 + 4 special angles, the same, direction off by 10°: 0.409Jellyfish, 6 + 4 special angles, the same, direction off by 20°: 0.409all 26 viewsJellyfish, all 26 views, outlines only: 0.537Jellyfish, all 26 views, exact depth: 0.624Jellyfish, all 26 views, depth from surface direction: 0.554Jellyfish, all 26 views, the same, direction off by 10°: 0.556Jellyfish, all 26 views, the same, direction off by 20°: 0.553Anglerfish6 straight viewsAnglerfish, 6 straight views, outlines only: 0.590Anglerfish, 6 straight views, exact depth: 0.723Anglerfish, 6 straight views, depth from surface direction: 0.596Anglerfish, 6 straight views, the same, direction off by 10°: 0.597Anglerfish, 6 straight views, the same, direction off by 20°: 0.5996 + 4 special anglesAnglerfish, 6 + 4 special angles, outlines only: 0.661Anglerfish, 6 + 4 special angles, exact depth: 0.770Anglerfish, 6 + 4 special angles, depth from surface direction: 0.686Anglerfish, 6 + 4 special angles, the same, direction off by 10°: 0.682Anglerfish, 6 + 4 special angles, the same, direction off by 20°: 0.682all 26 viewsAnglerfish, all 26 views, outlines only: 0.711Anglerfish, all 26 views, exact depth: 0.848Anglerfish, all 26 views, depth from surface direction: 0.754Anglerfish, all 26 views, the same, direction off by 10°: 0.756Anglerfish, all 26 views, the same, direction off by 20°: 0.736

Mean part overlap with the true model (1 = identical), every part counted once.

outlines onlyoutlines onlyexact depthexact depthdepth from surface directiondepth from surface directionthe same, direction off by 10°the same, direction off by 10°the same, direction off by 20°the same, direction off by 20°
0.00.10.20.30.4Flamingo6 straight viewsFlamingo, 6 straight views, outlines only: 0.006Flamingo, 6 straight views, exact depth: 0.006Flamingo, 6 straight views, depth from surface direction: 0.006Flamingo, 6 straight views, the same, direction off by 10°: 0.006Flamingo, 6 straight views, the same, direction off by 20°: 0.0076 + 4 special anglesFlamingo, 6 + 4 special angles, outlines only: 0.011Flamingo, 6 + 4 special angles, exact depth: 0.011Flamingo, 6 + 4 special angles, depth from surface direction: 0.011Flamingo, 6 + 4 special angles, the same, direction off by 10°: 0.012Flamingo, 6 + 4 special angles, the same, direction off by 20°: 0.015all 26 viewsFlamingo, all 26 views, outlines only: 0.018Flamingo, all 26 views, exact depth: 0.018Flamingo, all 26 views, depth from surface direction: 0.024Flamingo, all 26 views, the same, direction off by 10°: 0.033Flamingo, all 26 views, the same, direction off by 20°: 0.029Agama6 straight viewsAgama, 6 straight views, outlines only: 0.013Agama, 6 straight views, exact depth: 0.013Agama, 6 straight views, depth from surface direction: 0.014Agama, 6 straight views, the same, direction off by 10°: 0.014Agama, 6 straight views, the same, direction off by 20°: 0.0146 + 4 special anglesAgama, 6 + 4 special angles, outlines only: 0.021Agama, 6 + 4 special angles, exact depth: 0.021Agama, 6 + 4 special angles, depth from surface direction: 0.021Agama, 6 + 4 special angles, the same, direction off by 10°: 0.022Agama, 6 + 4 special angles, the same, direction off by 20°: 0.023all 26 viewsAgama, all 26 views, outlines only: 0.035Agama, all 26 views, exact depth: 0.035Agama, all 26 views, depth from surface direction: 0.036Agama, all 26 views, the same, direction off by 10°: 0.039Agama, all 26 views, the same, direction off by 20°: 0.042Scorpion6 straight viewsScorpion, 6 straight views, outlines only: 0.005Scorpion, 6 straight views, exact depth: 0.005Scorpion, 6 straight views, depth from surface direction: 0.013Scorpion, 6 straight views, the same, direction off by 10°: 0.011Scorpion, 6 straight views, the same, direction off by 20°: 0.0086 + 4 special anglesScorpion, 6 + 4 special angles, outlines only: 0.010Scorpion, 6 + 4 special angles, exact depth: 0.010Scorpion, 6 + 4 special angles, depth from surface direction: 0.168Scorpion, 6 + 4 special angles, the same, direction off by 10°: 0.145Scorpion, 6 + 4 special angles, the same, direction off by 20°: 0.119all 26 viewsScorpion, all 26 views, outlines only: 0.017Scorpion, all 26 views, exact depth: 0.017Scorpion, all 26 views, depth from surface direction: 0.299Scorpion, all 26 views, the same, direction off by 10°: 0.287Scorpion, all 26 views, the same, direction off by 20°: 0.271Octopus6 straight viewsOctopus, 6 straight views, outlines only: 0.003Octopus, 6 straight views, exact depth: 0.003Octopus, 6 straight views, depth from surface direction: 0.028Octopus, 6 straight views, the same, direction off by 10°: 0.018Octopus, 6 straight views, the same, direction off by 20°: 0.0136 + 4 special anglesOctopus, 6 + 4 special angles, outlines only: 0.006Octopus, 6 + 4 special angles, exact depth: 0.006Octopus, 6 + 4 special angles, depth from surface direction: 0.155Octopus, 6 + 4 special angles, the same, direction off by 10°: 0.114Octopus, 6 + 4 special angles, the same, direction off by 20°: 0.125all 26 viewsOctopus, all 26 views, outlines only: 0.009Octopus, all 26 views, exact depth: 0.009Octopus, all 26 views, depth from surface direction: 0.383Octopus, all 26 views, the same, direction off by 10°: 0.392Octopus, all 26 views, the same, direction off by 20°: 0.381Seahorse6 straight viewsSeahorse, 6 straight views, outlines only: 0.002Seahorse, 6 straight views, exact depth: 0.002Seahorse, 6 straight views, depth from surface direction: 0.006Seahorse, 6 straight views, the same, direction off by 10°: 0.007Seahorse, 6 straight views, the same, direction off by 20°: 0.0066 + 4 special anglesSeahorse, 6 + 4 special angles, outlines only: 0.004Seahorse, 6 + 4 special angles, exact depth: 0.004Seahorse, 6 + 4 special angles, depth from surface direction: 0.012Seahorse, 6 + 4 special angles, the same, direction off by 10°: 0.014Seahorse, 6 + 4 special angles, the same, direction off by 20°: 0.015all 26 viewsSeahorse, all 26 views, outlines only: 0.005Seahorse, all 26 views, exact depth: 0.005Seahorse, all 26 views, depth from surface direction: 0.021Seahorse, all 26 views, the same, direction off by 10°: 0.028Seahorse, all 26 views, the same, direction off by 20°: 0.032Racer snake6 straight viewsRacer snake, 6 straight views, outlines only: 0.016Racer snake, 6 straight views, exact depth: 0.016Racer snake, 6 straight views, depth from surface direction: 0.018Racer snake, 6 straight views, the same, direction off by 10°: 0.017Racer snake, 6 straight views, the same, direction off by 20°: 0.0186 + 4 special anglesRacer snake, 6 + 4 special angles, outlines only: 0.025Racer snake, 6 + 4 special angles, exact depth: 0.025Racer snake, 6 + 4 special angles, depth from surface direction: 0.029Racer snake, 6 + 4 special angles, the same, direction off by 10°: 0.028Racer snake, 6 + 4 special angles, the same, direction off by 20°: 0.066all 26 viewsRacer snake, all 26 views, outlines only: 0.034Racer snake, all 26 views, exact depth: 0.034Racer snake, all 26 views, depth from surface direction: 0.040Racer snake, all 26 views, the same, direction off by 10°: 0.055Racer snake, all 26 views, the same, direction off by 20°: 0.127Jellyfish6 straight viewsJellyfish, 6 straight views, outlines only: 0.008Jellyfish, 6 straight views, exact depth: 0.017Jellyfish, 6 straight views, depth from surface direction: 0.008Jellyfish, 6 straight views, the same, direction off by 10°: 0.008Jellyfish, 6 straight views, the same, direction off by 20°: 0.0086 + 4 special anglesJellyfish, 6 + 4 special angles, outlines only: 0.014Jellyfish, 6 + 4 special angles, exact depth: 0.031Jellyfish, 6 + 4 special angles, depth from surface direction: 0.016Jellyfish, 6 + 4 special angles, the same, direction off by 10°: 0.016Jellyfish, 6 + 4 special angles, the same, direction off by 20°: 0.014all 26 viewsJellyfish, all 26 views, outlines only: 0.025Jellyfish, all 26 views, exact depth: 0.048Jellyfish, all 26 views, depth from surface direction: 0.046Jellyfish, all 26 views, the same, direction off by 10°: 0.047Jellyfish, all 26 views, the same, direction off by 20°: 0.039Anglerfish6 straight viewsAnglerfish, 6 straight views, outlines only: 0.001Anglerfish, 6 straight views, exact depth: 0.001Anglerfish, 6 straight views, depth from surface direction: 0.001Anglerfish, 6 straight views, the same, direction off by 10°: 0.001Anglerfish, 6 straight views, the same, direction off by 20°: 0.0016 + 4 special anglesAnglerfish, 6 + 4 special angles, outlines only: 0.002Anglerfish, 6 + 4 special angles, exact depth: 0.002Anglerfish, 6 + 4 special angles, depth from surface direction: 0.004Anglerfish, 6 + 4 special angles, the same, direction off by 10°: 0.003Anglerfish, 6 + 4 special angles, the same, direction off by 20°: 0.005all 26 viewsAnglerfish, all 26 views, outlines only: 0.003Anglerfish, all 26 views, exact depth: 0.003Anglerfish, all 26 views, depth from surface direction: 0.005Anglerfish, all 26 views, the same, direction off by 10°: 0.013Anglerfish, all 26 views, the same, direction off by 20°: 0.071

Share of the true model's volume the carving cut away (0 = nothing true lost). Outline carving loses a little where the views disagree at the grid's resolution; depth must not add to it.

  • Exact depth: the overlap moves by +0.00 to +0.24 (rises in 23 of 24); true cells lost beyond the outline carving: at most 2.4% (jellyfish).
  • Depth from surface direction: the overlap moves by -0.15 to +0.04 (rises in 5 of 24); true cells lost beyond the outline carving: at most 37.4% (octopus).
  • The same, direction off by 10°: the overlap moves by -0.15 to +0.04 (rises in 5 of 24); true cells lost beyond the outline carving: at most 38.3% (octopus).
  • The same, direction off by 20°: the overlap moves by -0.17 to +0.03 (rises in 5 of 24); true cells lost beyond the outline carving: at most 37.2% (octopus).

The anglerfish's open mouth

outlines onlyoutlines onlyexact depthexact depthdepth from surface directiondepth from surface directionthe same, direction off by 10°the same, direction off by 10°the same, direction off by 20°the same, direction off by 20°
6 straight views6 straight views, outlines only: 75% still filled75% · outlines only6 straight views, exact depth: 56% still filled56% · exact depth6 straight views, depth from surface direction: 74% still filled74% · depth from surface direction6 straight views, the same, direction off by 10°: 74% still filled74% · the same, direction off by 10°6 straight views, the same, direction off by 20°: 74% still filled74% · the same, direction off by 20°6 + 4 special angles6 + 4 special angles, outlines only: 74% still filled74% · outlines only6 + 4 special angles, exact depth: 47% still filled47% · exact depth6 + 4 special angles, depth from surface direction: 69% still filled69% · depth from surface direction6 + 4 special angles, the same, direction off by 10°: 70% still filled70% · the same, direction off by 10°6 + 4 special angles, the same, direction off by 20°: 70% still filled70% · the same, direction off by 20°all 26 viewsall 26 views, outlines only: 73% still filled73% · outlines onlyall 26 views, exact depth: 23% still filled23% · exact depthall 26 views, depth from surface direction: 63% still filled63% · depth from surface directionall 26 views, the same, direction off by 10°: 62% still filled62% · the same, direction off by 10°all 26 views, the same, direction off by 20°: 62% still filled62% · the same, direction off by 20°

Share of the mouth's hollow still filled (0 = open as in the true model).

flamingo

Rows: the true model; then for 6 straight views and for all 26: outlines only, with exact depth, with depth from surface direction. Colours: the nearest true part.

carving by depth: flamingo
agama

Rows: the true model; then for 6 straight views and for all 26: outlines only, with exact depth, with depth from surface direction. Colours: the nearest true part.

carving by depth: agama
scorpion

Rows: the true model; then for 6 straight views and for all 26: outlines only, with exact depth, with depth from surface direction. Colours: the nearest true part.

carving by depth: scorpion
octopus

Rows: the true model; then for 6 straight views and for all 26: outlines only, with exact depth, with depth from surface direction. Colours: the nearest true part.

carving by depth: octopus
seahorse

Rows: the true model; then for 6 straight views and for all 26: outlines only, with exact depth, with depth from surface direction. Colours: the nearest true part.

carving by depth: seahorse
racer snake

Rows: the true model; then for 6 straight views and for all 26: outlines only, with exact depth, with depth from surface direction. Colours: the nearest true part.

carving by depth: racer snake
jellyfish

Rows: the true model; then for 6 straight views and for all 26: outlines only, with exact depth, with depth from surface direction. Colours: the nearest true part.

carving by depth: jellyfish
anglerfish

Rows: the true model; then for 6 straight views and for all 26: outlines only, with exact depth, with depth from surface direction. Colours: the nearest true part.

carving by depth: anglerfish

2. The fitted tubes, without the steps

The branching-tube fit is smooth: a bent centre line with round sections that grow and shrink along it. It was turned into a mesh by testing inside or outside at each point of a grid, which put the surface on the grid's steps. Now it is meshed from how far each point is inside or outside, which follows the curve. Nothing is refitted. On the seven true models (66 parts), the branching tube is the best of the five tools for 17 parts as fitted and 21 re-meshed. For thick parts the score barely moves (the steps were small next to the fit's own error), but the jellyfish's thin tentacles, which the old grid's steps had broken up, now come out whole: three tentacle parts that had been fitted best by a flat sheet are now fitted best by tubes. Parts within the pass line: 43 before, 44 after.

octopus
stepped and smooth fits: octopus
jellyfish
stepped and smooth fits: jellyfish
scorpion
stepped and smooth fits: scorpion
flamingo
stepped and smooth fits: flamingo
agama
stepped and smooth fits: agama
seahorse
stepped and smooth fits: seahorse
racer snake
stepped and smooth fits: racer snake

3. AI pictures from more angles

Each animal's sheet (front, left side, back, top), plus its right side and underside drawn as separate pictures. The per-part pick carves a shape from these six, and four special angles are chosen per animal from that shape, each for the parts whose surface the straight views leave least certain (named under each angle). The image model draws the angles only roughly: compared with the asked-for camera, a picture's width-to-height disagrees by 2% to 57%, and the pick drops a picture for the parts where it disagrees.

The four special angles are drawn for the jellyfish, racer snake, scorpion and seahorse. For the agama, flamingo and octopus they are not drawn yet: a bug of mine in the first choice of angles (it undercounted how much of each picture the shape kept, so it chose for the wrong shape) sent those three to the image model with other angles. Those pictures are kept, but they are not the special angles. Fits to the AI pictures are running on the lab.

scorpion
AI pictures: scorpion
jellyfish
AI pictures: jellyfish
seahorse
AI pictures: seahorse
racer snake
AI pictures: racer snake
flamingo
AI pictures: flamingo
agama
AI pictures: agama
octopus
AI pictures: octopus