Mumbai University > Mechanical Engineering > Sem 7 > CAD/CAM/CAE

Marks: 10M

Year: May 2012, Dec 2012

In hidden-line removal, edges or other vectors in the model that are obscured by visible surfaces are omitted from the display of the image, or displayed as dashed rather than full lines. An alternative name for the technique is visible line identification. Some of the common hidden line algorithms are

• Floating horizon
• Image space
• List priority
• Object space
• Ray tracing
• Roberts Warnock

Floating Horizon Algorithm

Floating Horizon Algorithm is most commonly used for representation of 3D surfaces of the form F(x,y,z) = 0. The technique is to convert 3D problem to equivalent 2D problem by intersecting 3D surface with a series of parallel cutting planes at constant values of the coordinate in the view direction. It could be x, y or z. The function F(x,y,z)=0 is reduced to a planar curve in each of these parallel planes y=f(x,z). It is assumed that the curves are single valued functions of independent variables and the result is projected on to the z=0 plane. The algorithm first sorts the z=constant planes in increasing distance from the viewpoint beginning from z=0 (closest to viewpoint)

• Upper Horizon: If at any given value of x, the y value of the curve in the current plane is larger than the y value for any previous curve at that z value, then the curve is visible, otherwise hidden.
• Lower Horizon: If at any given value of x, the y value of the curve in the current plane larger than the maximum y value or smaller than the minimum y value for any previous curve at that z plane then the curve is visible, else hidden.

The algorithm assumes the value of y is available at every x location. However, if it is not available (crossing of curves), a linear interpolation of known values is calculated to fill the upper and lower floating horizon arrays.

If the function contains very narrow regions (small increments of x) then the algorithm yields incorrect results. The effect is generally caused by computing the function for visibility at a resolution less than that of image space resolution. The problem is overcome by taking more points to evaluate the function in narrow regions.