BezierView

BezierView (short bview) is a light weight viewer that renders Bezier patches, rational bezier patches and polygonal meshes. It provides a simple tool to analyse surfaces based on curvature plots, curvature needle plots, and highlight line plots. Currently, the WebGL version is recommended but also binaries and source coode are available.

Features

Tensor product Bezier patches
Tensor product rational patches
Triangle Bezier patches
Polyhedron
PN triangles, PN quadrilateral patches
Gaussian/Mean/Max/Min curvature plot (set min: max: in file IN.crvBounds)
Plane clipping
Position save/load
Object groups different colors can be assigned to different groups
Environment mapping (Image file: room.bmp)

Curvature

Clipping

Patch Grouping

Example Data

patches
- tensor-product (quad) patches: hex.bv hex2.bv tp2x1.bv tp3x3.bv
- rational quad patches: rat1.bv tor.bv sphere.bv
- triangular patches: tri1.bv tri2.bv
- rational triangular patches: air2.bv tet2.bv mix2.bv
utal teapot teapot.bv teapot2.bv tpt_grp.bv
polyhedron data cube.bv closedcone.bv hand.bv tetra.bv
mixed data tp_poly.bv
grouped data tpt_grp.bv tridat.cube
g2 surfaces plm.icosa.260 plm.tw.700 plm.oct.100 cubeg2.bv twg2.bv

File format

A .bv file consists of segments. Each segment has a patch header followed by the patch data. The header starts with the

Patch type:

1: polyhedron
3: triangular patch
4: tensor-product patch with same degree in both directions.
5: general tensor-product patch
8: rational Bezier tensor-product
9: PN triangle patches
10: PN quads patches
11: rational triangular patches

Polyhedron

essentially .obj format

1
Vnum Fnum
v0x v0y v0z
v1x v1y v1z
..
v(n-1)x v(n-1)y v(n-1)z
3 f1v1 f1v2 f1v3   (OR: 4 f1v1 f1v2 f1v3 f1v4)
...
3 fmv1 fmv2 fmv3    (vertices are indeexed 0..n-1, not 1..n])

Note: User can use obj2bv to convert .obj into .bv file.
(obj2bv also shows how to display control polygon and BB-patch in BView at the same time)

Tensor-product (4-sided) patches

header one of:

5
deg_u deg_v

Group 1 deg2x3
5
2 3
-1.5 1.0 0.0
-0.5 1.0 0.0
0.5 1.0 0.0
1.5 1.0 0.0
-1.5 0.0 0.0
-0.5 0.0 0.5
0.5 0.0 0.5
1.5 0.0 0.0
-1.5 -1.0 0.0
-0.5 -1.0 0.0
0.5 -1.0 0.0
1.5 -1.0 0.0

(Example of deg_u = 2 & deg_v = 3 patch)

or when deg = deg_u = deg_v

4
deg

Group 0 Bi-3
5
3 3
-1.5 1.5 0.0
-0.5 1.5 0.0
0.5 1.5 0.0
1.5 1.5 0.0
-1.5 0.5 0.0
-0.5 0.5 0.5
0.5 0.5 0.5
1.5 0.5 0.0
-1.5 -0.5 0.0
-0.5 -0.5 0.5
0.5 -0.5 0.5
1.5 -0.5 0.0
-1.5 -1.5 0.0
-0.5 -1.5 0.0
0.5 -1.5 0.0
1.5 -1.5 0.0

(Example of deg = deg_u = deg_v = 3 patch)

8
deg_u deg_v

The patch data are x y z values of the control points in row-major order. If rows= deg_u+1 =du1 and columns= deg_v+1 = dv1:

p(1,1) p(1,2) .... p(1,dv1)

p(2,1) p(2,2) .... p(2,dv1)

.. .. .... ..

p(du1,1) p(du1,2) .. p(du1,dv1)

and p has coordinates x,y,z then

x(1,1) y(1,1) z(1,1)
x(1,2) y(1,2) z(1,2)
 :
x(du1,dv1) y(du1,dv1) z(du1,dv1)

For example a tensor-product patch of degree 1 by 2 has the header

Total-degree (3-sided) Bezier patches

header:

3
deg

followed by (deg+2)*(deg+1)/2 control points with row-ascending ordering. For a cubic patch

7 8

4 5 6

0 1 2 3

the coordinates x,y,z of the patch data are

x(0) y(0) z(0)
x(1) y(1) z(1)
  :
x(9) y(9) z(9)

PN triangle patches

header:

9
deg Ndeg

control points as 3-sided patch followed by normals as 3-sided patch.

PN quads

header:

10
degu degv Ndegu Ndegv

then the control points; then the normals arranged at the same order

License

This program is free for educational/research purpose. You will need to gain permissions from authors before you can use this program or any part of the source code for commercial usage.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY.

Author(s):

Jorg Peters
Xiaobin Wu
Michael Malkiewicz, Param Gupta (webGL)