The proposed algorithm d/splays the projected surface F as a quadrilateral grid of straight segments, g; any one of these can be part of the silhouette if, and only if, the two patches connected along g lie on the same side of it. The same segment g is drawn, if it is not hidden by remote patches. The algorithm can be applied to any surface regular or not and self-intersecting and can display the entire silhouette or apart of it. It is simple, it uses only the rectangular coordinates of the projected vertices of the grid and requires few elementary mathematical operations.
mathematics, algorithms, silhouettes
Suppose that a dark figure, geometrical or not, is drawn on a white background; the silhouette of the plane figure is the line that separates the dark design from the light background. Similarly, when one eye is focussed on an opaque dark body, Y, shown against a light background, it is seen as a dark figure outlined by a line G, which separates the dark region from the background. G is the silhouette of the spatial body F, and as it is only a 'visual' line, it will disappear when the eye is closed. However, it can be permanently recorded as a real line G* by using a normal camera to take a picture of I ~, so that the camera's focus and the eye's focus would coincide. Geometrically speaking, the line G* is the surface's projection from the camera's focus onto its flat film. Following this pattern the algorithm projects [' from a single point (perspective projection); or in a parallel direction (axonometric projection), on a particular projection plane p.
Because it is graphically impossible to project all the points of F, F is approximated to a quadrangular grid of straight segments and then those vertices of the grid, belonging to F, are projected on p.
The most important features of the algorithm are detailed in the following.