We already mentioned that good visual approximations of trees should display the fringed character of the foliage. If only a few large-sized polygons are used, the desired look is not achieved, not even if partially transparent textures are used.
It is more efficient to represent the foliage deliberately using unconnected prim- point-based representation ^ itives. Since leaves mostly correspond to small discrete objects, points can be
used instead of polygons. That way the already-mentioned geometric overspecification can be decreased. For example, such an overspecification occurs when for one million pixels (image size is approximately 1000×1000), 100 million polygons are used for rendering. This will result in many polygons per pixel that are processed and only one that finally can be seen.
Thus, for a fast rendering, the visible image information must be determined in an efficient manner, so that later the geometry can also be stored and rasterized efficiently. Points offer this advantage, especially if the visual size of the object to be represented does not need too many pixels onscreen. In a dynamic LOD
rendering that decision must be made individually for each object relative to the representation in which the image can be computed in the most efficient way.
The capability of contemporary graphics hardware together with such dynamic methods of representation is best characterized through the vertex rate at which the geometric information can be transferred from the processor to the graphics chip where rasterized. This is an important aspect, because most graphics processors achieve their best values when processing static information. For a dynamic representation, however, all information must be newly processed from the start.
The connection and rasterization of two vertices to a line or of three vertices to a triangle is for smaller objects an almost constant factor, so that an efficient description of the data produces a given scene most optimally through a coordinated mixing of point – and line-based representations with polygonal data, and where a minimum of vertices are transferred.
One of the first studies in which such a mixture was used for the rendering of trees was proposed by Weber and Penn . They divided trees into lines and points, whereby the lines approximated the branching structure, and the points approximated the foliage. The points were produced through the analysis of the leaf distributions along the trunk. For this, clusters of leaves were defined and replaced with geometric points. Figure 10.5 shows a LOD approximation of a tree as well as a synthetic landscape.