File: SVVector2dImpl.mesa
Last edited by Bier on June 1, 1984 4:36:10 pm PDT
Author: Eric Bier on January 28, 1987 2:26:31 pm PST
Contents: Routines for manipulation vectors in two dimensions
DIRECTORY
RealFns, SV2d, SVAngle, SVVector2d;
SVVector2dImpl: CEDAR PROGRAM
IMPORTS RealFns, SVAngle
EXPORTS SVVector2d =
BEGIN
Point2d: TYPE = SV2d.Point2d;
TrigLineSeg: TYPE = SV2d.TrigLineSeg;
Vector2d: TYPE = SV2d.Vector2d;
VectorFromPoints:
PUBLIC
PROC [tail, head: Point2d]
RETURNS [vector: Vector2d] = {
vector[1] ← head[1] - tail[1];
vector[2] ← head[2] - tail[2];
};
VectorFromAngle:
PUBLIC
PROC [angle:
REAL]
RETURNS [vector: Vector2d] = {
angle must be in degrees in the range: -180 < angle <= 180.
vector is a unit vector.
vector[1] ← RealFns.CosDeg[angle];
vector[2] ← RealFns.SinDeg[angle];
};
VectorPlusAngle:
PUBLIC
PROC [v: Vector2d, degrees:
REAL]
RETURNS [rotatedV: Vector2d] = {
Find angle of v. This should be easy. Normalize v and its components will be cos(theta), sin(theta) respectively.
theta: REAL ← RealFns.ArcTanDeg[v[2], v[1]];
angleSum: REAL ← theta + degrees;
IF angleSum<= -180 THEN angleSum ← angleSum + 360
ELSE IF angleSum > 180 THEN angleSum ← angleSum - 360;
rotatedV ← VectorFromAngle[angleSum];
};
AngleFromVector:
PUBLIC
PROC [v: Vector2d]
RETURNS [position:
REAL] = {
position is a position angle such that -180 < position <= 180
position ← SVAngle.ArcTan[v[2], v[1]];
};
AngleCCWBetweenVectors:
PUBLIC
PROC [v1, v2: Vector2d]
RETURNS [difference:
REAL] = {
difference will be in: 0 <= difference < 360. A clockwise angle
angle1, angle2: REAL;
angle1 ← AngleFromVector[v1];
angle2 ← AngleFromVector[v2];
difference ← SVAngle.CounterClockwiseAngle[angle1, angle2];
};
AngleCWBetweenVectors:
PUBLIC
PROC [v1, v2: Vector2d]
RETURNS [difference:
REAL] = {
difference will be in: 0 <= difference < 360. A counter-clockwise angle
angle1, angle2: REAL;
angle1 ← AngleFromVector[v1];
angle2 ← AngleFromVector[v2];
difference ← SVAngle.ClockwiseAngle[angle1, angle2];
};
SmallestAngleBetweenVectors:
PUBLIC
PROC [v1, v2: Vector2d]
RETURNS [difference:
REAL] = {
all angles in degrees. RETURNS ClockwiseAngle or CounterClockwiseAngle. Whichever is smaller. -180 < difference <= 180.
angle1, angle2: REAL;
angle1 ← AngleFromVector[v1];
angle2 ← AngleFromVector[v2];
difference ← SVAngle.ShortestDifference[angle1, angle2];
};
Add:
PUBLIC
PROC [v1, v2: Vector2d]
RETURNS [v1PlusV2: Vector2d] = {
v1PlusV2[1] ← v1[1] + v2[1];
v1PlusV2[2] ← v1[2] + v2[2];
};
Sub:
PUBLIC
PROC [v1, v2: Vector2d]
RETURNS [v1MinusV2: Vector2d] = {
v1MinusV2[1] ← v1[1] - v2[1];
v1MinusV2[2] ← v1[2] - v2[2];
};
Scale:
PUBLIC
PROC[v: Vector2d, s:
REAL]
RETURNS [vTimesS: Vector2d] = {
vTimesS[1] ← v[1]*s;
vTimesS[2] ← v[2]*s;
};
Normalize:
PUBLIC
PROC [v: Vector2d]
RETURNS [normV: Vector2d] = {
mag: REAL ← Magnitude[v];
normV[1] ← v[1] / mag;
normV[2] ← v[2] /mag;
};
Negate:
PUBLIC PROC [v: Vector2d]
RETURNS [negV: Vector2d] = {
negV[1] ← -v[1];
negV[2] ← -v[2];
};
ElementwiseProduct:
PUBLIC
PROC [v1, v2: Vector2d]
RETURNS [v1Timesv2: Vector2d] = {
v1Timesv2[1] ← v1[1]*v2[1];
v1Timesv2[2] ← v1[2]*v2[2];
};
DotProduct:
PUBLIC
PROC [v1, v2: Vector2d]
RETURNS [scalar:
REAL] = {
scalar ← v1[1]*v2[1] + v1[2]*v2[2];
};
Magnitude:
PUBLIC
PROC [v: Vector2d]
RETURNS [mag:
REAL] = {
mag ← RealFns.SqRt[v[1]*v[1] + v[2]*v[2]];
};
Distance:
PUBLIC
PROC [p1, p2: Point2d]
RETURNS [dist:
REAL] = {
dist ← Magnitude[Sub[p2, p1]];
};
MagnitudeSquared:
PUBLIC
PROC [v: Vector2d]
RETURNS [magSquared:
REAL] = {
magSquared ← v[1]*v[1] + v[2]*v[2];
};
DistanceSquared:
PUBLIC
PROC [p1, p2: Point2d]
RETURNS [distSquared:
REAL] = {
distSquared ← MagnitudeSquared[Sub[p2, p1]];
};
RightNormalOfTrigLineSeg:
PUBLIC
PROC [seg: TrigLineSeg]
RETURNS [normal: Vector2d] = {
Given the ordered points of the line segment, we can find the vector from the first to the second. If this vector is [a, b] then the vector 90 degrees to the right is [b, -a];
direction: Vector2d;
IF seg.pLoIsFirst THEN direction ← VectorFromPoints[tail: seg.pLo, head: seg.pHi]
ELSE direction ← VectorFromPoints[tail: seg.pHi, head: seg.pLo];
normal[1] ← direction[2];
normal[2] ← -direction[1];
};
LeftNormalOfTrigLineSeg:
PUBLIC
PROC [seg: TrigLineSeg]
RETURNS [normal: Vector2d] = {
Given the ordered points of the line segment, we can find the vector from the first to the second. If this vector is [a, b] then the vector 90 degrees to the left is [-b, a];
direction: Vector2d;
IF seg.pLoIsFirst THEN direction ← VectorFromPoints[tail: seg.pLo, head: seg.pHi]
ELSE direction ← VectorFromPoints[tail: seg.pHi, head: seg.pLo];
normal[1] ← -direction[2];
normal[2] ← direction[1];
};
END.