![]() Orientation must be solved before determining location. Intuitively and visually, L is the signed distance of the line from the origin (with positive distance increasing along direction o). The 2nd feature of a 2D line represented this way is its location L. Numerical algorithms benefit by avoiding such ill-behaved exceptions (e.g. Orientation o has the advantage of not overcompressing the information vested in dx and dy into a single scalar as slope does, avoiding the need to appeal to infinity as a value. O ← ( dy, -dx ) norm = ( dy, -dx ) / || ( dy, -dx ) || (orientation of a 2D line) ![]() The orientation is computed using the same two quantities dx and dy that go into computing slope m: O is the line's orientation, a normalized direction vector (unit vector) pointing perpendicular to its run direction. Here, the line is represented by two features: o and L. Īn example of a predicate form of the vector line equation in 2D is: If you substitute a known point into the above equation, it cannot be evaluated for equality because t was not supplied, only p. However, in order to function as a predicate, the representation must be sufficient to easily determine ( T / F ) whether any specified point p is on the line. ![]() Points may be generated along the line given values for a, t and v: The line equation a+t v is a generative form, but not a predicate form. In Euclidean space (any number of dimensions), given a point a and a nonzero vector v, a line is defined parametrically by ( a+t v), where the parameter t varies between -∞ and +∞.
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