File: Angles2d.mesa
Copyright Ó 1992 by Xerox Corporation. All rights reserved.
Last edited by Bier on June 4, 1985 6:14:56 pm PDT
Author: Eric Bier on February 9, 1987 4:59:33 pm PST
Contents: Gargoyle requires a precise set of angle operations defined with angle "theta" in the range -180 < theta <= 180. "theta" is an absolute angle (ie a position around the circle measured from the positive x axis). Given two positions angles T1 and T2 we can find the incremental clockwise angle CT between them or the incremental counter-clockwise angle CCT where -360 < CT <= 0 and 0 <= CCT < 360. When we add two angles, we are adding an incremental angle to a position angle to get a new position angle. We subtract two position angles to get an incremental angle. All angles are in degrees.
Pier, December 6, 1985 10:01:09 am PST
Angles2d: CEDAR DEFINITIONS =
BEGIN
Normalize: PROC [anyRange: REAL] RETURNS [range180: REAL];
Takes an angle in degrees and puts it in -180 < theta <= 180 form.
AsSlope: PROC [anyRange: REAL] RETURNS [pos180: REAL];
Takes an angle in degrees and puts it in 0 <= theta < 180 form. This may require adding 180 degrees for negative angles.
Add: PROC [position, increment: REAL] RETURNS [finalPosition: REAL];
All angles in degrees
ClockwiseAngle: PROC [fromPosition, toPosition: REAL] RETURNS [increment: REAL];
All angles in degrees. -360 < increment <= 0
CounterClockwiseAngle: PROC [fromPosition, toPosition: REAL] RETURNS [increment: REAL];
All angles in degrees. 0 <= increment < 360.
For example, if the clockwise angle is -90, the counter-clockwise angle will be 270.
ShortestDifference: PROC [position1, position2: REAL] RETURNS [pos1MinusPos2: REAL];
All angles in degrees. RETURNS ClockwiseAngle or CounterClockwiseAngle. Whichever is smaller. -180< pos1MinusPos2 <= 180.
Scale: PROC [angle: REAL, scalar: REAL] RETURNS [angleTimesScalar: REAL];
All angles in degrees. Think of angle as the increment from 0 degrees to angle degrees. Scale this and normalize.
ArcTan: PROC [numerator, denominator: REAL] RETURNS [degrees: REAL];
Has the effect of calling RealFns.ArcTanDegrees and normalizing the result.
IsInCCWInterval: PROC [testPosition: REAL, fromPosition, toPosition: REAL] RETURNS [BOOL];
IsInCCWInterval2: PROC [testPosition: REAL, fromPosition, increment: REAL] RETURNS [BOOL];
Consider the set of angles encountered when traveling counterclockwise from angle "fromPosition" to angle "toPosition" around a circle. Is testPosition one of the angles encountered?
AlmostParallel: PROC [pos1, pos2: REAL, epsilon: REAL] RETURNS [BOOL];
pos1 and pos2 are assumed to be in -180 < theta <= 180. Return TRUE if they are the same angle +- epsilon or if they differ by 180+- epsilon.
END.