2D hair distribution map

Trigonometrical prism wisp model and 2D hair distribution map

Hairstyle

Trigonometrical prism wisp model

We define our hair model, the trigonometrical prism Wis model, as follows. First, all the hair is divided into several groups of wisps, according to the position on the skull. Each wisp is constructed by continuous trigonometrical prisms, as shown in Fig. 1. The trigonometrical prisms within one wisp are linked by three 3D B-spline curves. The numbers of control points may differ, basically according to the length of the strand of hair. Using curves to implement hair is a very intuitive idea. It enables our system to create the physical properties of hair easily. Furthermore, because hair strands within a wisp are grouped, we can successfully reduce the computational time. This modeling method keeps the hair style data simple and organized. Thus, it is very flexible for the various hair styles.

2D Hairstyle

What has to be noted here is the cross-section of the wisp's silhouette: the actual image of one wisp is determined by its 2D distribution map, which we will explain later in this section. The trigonometrical construction of our trigonometrical prism wisp model does not affect the real shape of synthesized wisps. The cross-section of wisp's silhouette does need to be a triangle. Its shape is controlled by the 2D hair distribution maps that we assign to the wisp.

Two-dimensional hair distribution map

Mans Hairstyle

We use 2D arrays to define the distribution of hair strands on the cross-section of one wisp, as shown in Fig. 2. Through the continuous trigonometrical prisms of one wisp, these 2D points are projected onto screen according to each pair of vectors on the edges of the two triangles. The position of each hair strand within a wisp is actually determined in this 2D way. It is noted that this 2D hair NM distribution map can be defined to have hair distribution outside the triangle cross-section of the triangle prism. This allows us to remove the discontinuity of hair distribution among wisps. However, we need only calculate the three control lines that we use to control the trigonal prisms.

Hair Treatment

Thus, the 2D hair distribution maps contribute to reduce the computational cost of rendering hair. There is another important issue: the application of the 2D distribution  maps to our system for the control of the shape of a wisp's silhouette. For example, if the hair on the 2D map is randomly distributed within a triangle or a circle, the basic shape of the synthesized wisp will be a curved trigonometrical prism or a curved cylinder, respectively. By controlling the shape and distribution density of the 2D distribution maps, we can create a natural and rich effect on 3D hair forms.