Geometry

8.1

Geometry

(require "../../racket/ctf/vector.rkt")

package: base

Note: if you are using this code, it is assumed you will be working in (radians-mode)

1 Vector

To use vectors, make sure to put (require "../../racket/ctf/vector.rkt") at the top of your file.

procedure
(vec x y) → vec?
x : number?
y : number?

procedure
(vec-x vec) → number?
vec : vec?

procedure
(vec-y vec) → number?
vec : vec?

(vec x y) will return a value with the given x and y stored in it. You can then get out those values using vec-x and vec-y. For example (vec-y (vec 1 2.5)) returns 2.5.

procedure
(vec-add vec1 vec2) → vec?
vec1 : vec?
vec2 : vec?

Returns a new vector which is the sum vec1 and vec2

procedure
(vec-sub vec1 vec2) → vec?
vec1 : vec?
vec2 : vec?

Returns a new vector which is vec1 minus v2

procedure
(vec-scale vec c) → vec?
vec : vec?
c : number?

Returns a new vector which is vec1 scaled the c

procedure
(rotate vec angle) → vec?
vec : vec?
angle : number?

Returns a new vector that is vec rotated angle radians to the right

procedure
(polar r angle) → vec?
r : number?
angle : number?

Returns a vector whose magnitude is r and whose angle with the positive x-axis is angle

procedure
(angle-of vec) → number?
vec : vec?

Returns the angle that vec makes with the positive x-axis

procedure
(mag vec) → number?
vec : vec?

Returns the magnitude of vec

procedure
(dist vec1 vec2) → number?
vec1 : vec?
vec2 : vec?

Returns the distance between vec1 and vec2

2 Line Like

To use line like, make sure to put (require "../../racket/ctf/ll.rkt") at the top of your file.

A "line like" (not a real term) is any shape that is a subset of a single line. The three that we are dealing with are: - Lines - Rays - Line Segments When we say line like, or ll, we are referring to any one of these 3 shapes.

procedure
(line-pp p1 p2) → ll?
p1 : vec?
p2 : vec?

Returns a line like that is treated as the line that goes through p1 and p2

procedure
(line-pa p angle) → ll?
p : vec?
angle : number?

Returns a line like that is treated as the line that starts at p, and travels in the direction of the given angle

procedure
(ray-pa p angle) → ll?
p : vec?
angle : number?

Returns a line like that is treated as the ray that starts at p, and travels in the direction of the given angle

procedure
(line-segment-pp p1 p2) → ll?
p1 : vec?
p2 : vec?

Returns a line like that is treated as the line segment with ends at p1 and p2

procedure
(angle-of-ll ll) → number?
ll : ll?

Returns the angle above or below the positive x-axis of the line. The value of angle-of-ll will always be in [-90,90)

procedure
(ll-p1 ll) → vec?
ll : ll?

Returns one point on the line like. If it’s a line segment or a ray it will be one of its end points.

procedure
(ll-p2 ll) → vec?
ll : ll?

Same as ll-p1 except