Surface reconstruction | Animation | Surface retouching | Image Inpainting | Metamorphosis | Surface blending | Sketching | Smoothing |

- define a nearest plane by determining normal for each polygon and then averaging them at shared points
- apply such a rotation to the neighbor points that the nearest plane is perpendicular to z-direction,
- calculate differences or deviations for local z-directions that define the inverse mapping function,
- apply transformation for the selected point and
- produce inverse rotation of the calculated point.
To define the inverse mapping function different number of vertices N can be used for interpolation. The bigger number N we select the more feature-preserving smoothing will be performed.
# Examples

**Shape Smooth Examples**:

**STANFORD BUNNY:**

(a)

(d)

(c)

(d)**Figure.**(a) The original Stanford Bunny model, (b) Smoothed model after one iteration based on 11 points interpolation, (c) Smoothed model after one iteration based on 5 points interpolation, (d) Smoothed model after 5 iterations based on 5 points interpolation.**Stanford Bunny model****(35947 vertices, 69451 polygons).**

Download: source model in *.vtk

file format (2.5 MiB).Root Mean Square Error (RMS) Processing timeÂ 11 points/1 iteration 0.00177134 4.756 sec. 5 points/1 iteration 0.000634002 3.405 sec. 5 points/5 iterations 0.00229198 15.547 sec. **MOAI:**

(a)

(b)

(c)**Figure.**(a) - Smoothed Moai model with real-world noiseÂ (see Surface Retouching section) after one iteration based on 3 points interpolation, (b) Smoothed modified Moai model (see Surface Retouching section) after one iteration based on 3 points interpolation, (c) Smoothed modified Moai model after 5 iterations based on 3 points interpolation.**Moai model****(10002 vertices, 20000 polygons).**

Download: source original model in *.vtk file format (673 Kib),

source modified model in *.vtk file format (673 KiB).Root Mean Square Error (RMS) Processing timeÂ 3 points/1 iteration 0.00139069 0.891 sec. 3 points/5 iterations 0.00294161 4.345 sec.

# Demo software

**Shape Smooth**:**Note:**This program was compiled for Microsoft Windows and can be used on any PC with Microsoft Windows 9x, Me, NT, 2000 or XP installed. Before running this program you need to download and install VTK runtime library VTK Core (2.8 MiB), if you have not done it already.Shape Smooth: program to smooth polygonal data.

**Usage:**shapesmooth.exe file.vtk N_of_points_in_interpolation K_iterations.

**Download:**exe, 82 KiB.**Download example data (all examples):**exe, 4.7 MiB.