2004
DOI: 10.1016/j.cagd.2003.07.011
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Single equation without inequalities to represent a composite curve

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Cited by 8 publications
(2 citation statements)
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“…It consists of two stages: the first stage is the pre-optimization stage, in which an initial path is developed between the start and the target points guided with the edges of the obstacles. To develop this pre-optimization path, a straight line is developed based on the Heaviside unit step [58] between the start and target points. further, a mathematical equation is developed based on the Heaviside step function to describe the complete shape of obstacles in the environment.…”
Section: A Problem Statementmentioning
confidence: 99%
“…It consists of two stages: the first stage is the pre-optimization stage, in which an initial path is developed between the start and the target points guided with the edges of the obstacles. To develop this pre-optimization path, a straight line is developed based on the Heaviside unit step [58] between the start and target points. further, a mathematical equation is developed based on the Heaviside step function to describe the complete shape of obstacles in the environment.…”
Section: A Problem Statementmentioning
confidence: 99%
“…Some research (e.g., Milenkovic, 1993) has addressed the problem of polygon modelling but the models are mostly in two-dimensional (2D) and the models and their associated constraints often consist of inequalities. Chicurel-Uziel (2004) proposed a generalized 3D model for polygonal prisms without inequality but the x and y coordinates are modelled and estimated separately using two equations and they cannot be readily expressed in terms of the other. Also, no inclinations of the prism were considered in its model.…”
Section: Introductionmentioning
confidence: 99%