Defined quadrilateral mesh
- Quadrilateral mesh, as the name implies, it is a patch of each quadrilateral mesh. Sometimes, there will be doping quadrilateral mesh of some triangle patch, we are called to this type of grid also quadrilateral mesh. Triangle mesh inverse modeling is common in the art, such as obtained by the three-dimensional scanner grid. Common quadrilateral mesh in the forward modeling systems, such as 3dsMax, ZBrush like. This is mainly because a triangular mesh or point cloud turn into quadrilateral mesh with some difficulty, particularly quality quadrilateral meshes.
- Regular point: the point - of degree 4; boundary point (non inflection (Corner)) - 3 degrees; boundary point (convex inflection) - 2 degrees; boundary point (concave inflection) - 4 degrees
- Category: mainly be classified according to the regular degree vertices. As shown below, the first type is a regular mesh grid, all the vertices of degree 4, and only the special mesh topology to achieve regular; second category is semi-regular grid, which is a regular slice; Third category is semi-regular grid in degrees, most of the degree of its vertices 4; last category is disordered quadrilateral mesh, it has a lot of non-regular dot.
The advantages and disadvantages of the quadrilateral mesh
Compared with the triangular mesh, quadrilateral mesh has several advantages:
- Edge alignment features: quadrilateral edge mesh may be naturally aligned with the feature edges, to side and can be naturally aligned to the geometric features of the model.
- Spline surfaces and subdivision surfaces: spline surfaces and Catmull-Clark subdivision surfaces common domain is quadrilateral
- Textures: the semi-regular quadrilateral mesh, each piece can be a good regular aligned with the picture, the picture in favor of sampling accuracy
While the quadrilateral mesh have some disadvantages:
- It may not be co-planar quadrangular
High quality quadrilateral mesh
- The number of singular points as little as possible, rational layout
- Side face sheet to be aligned with the geometric features Trend
- Uniform in side length, or adaptive geometric feature
A method of generating a quadrilateral mesh
Forward modeling software can create a quadrilateral mesh directly. Inverse modeling grid generally triangular mesh, triangular mesh need for a method to turn into a quadrilateral mesh
- Catmull-Clark subdivision triangle can be a quadrilateral mesh, its quality is relatively low, singular points, edges toward bad. Some methods may be applied subsequent optimization quadrilateral mesh
- Parametric approach
- Morse-Smale complex method
- After the mesh segmentation method Parametric Patches
Processing quadrilateral mesh
- Mesh simplification
- Geometry Optimization
- Higher-order surface fitting, subdivision surface fitting
- Mesh topology optimization
Interested readers are welcome to reference video version