<*PRAGMA LL*>A

`Path.T`

is a sequence of straight and curved line segments,
suitable for stroking or filling.
A {\it segment} is a directed arc in the Cartesian plane determined
by two cubic polynomials `h(t)`

, `v(t)`

, where `t`

ranges over the
interval of real numbers `[0, 1]`

. The segment is said to {\it start}
at `(h(0), v(0))`

and {\it end} at `(h(1), v(1))`

. If `h`

and `v`

are linear functions of `t`

, then the segment is {\it linear}: it
consists of a line segment. If `h`

and `v`

are constant functions of
`t`

, then the segment is {\it degenerate}: it consists of a single
point.

The segments of a path are grouped into contiguous {\it subpaths}, which can be {\it open} or {\it closed}. Within a subpath, each segment starts where the previous segment ends. In a closed subpath, the last segment ends where the first segment starts. (This may also happen for an open subpath, but this coincidence does not make the subpath closed.)

The {\it current point} of a path is the endpoint of the last segment of its last subpath, assuming this subpath is open. If the path is empty or if the last subpath is closed, the current point is undefined.

INTERFACEThe callPath ; IMPORT Point, Rect; TYPE T <: ROOT;

`NEW(Path.T)`

creates an empty path.
PROCEDURE Reset(path: T);

Set`path`

to be empty.

PROCEDURE MoveTo(path: T; READONLY p: Point.T);

Extend`path`

with a new degenerate segment that starts and ends at`p`

. This begins a new subpath.

PROCEDURE LineTo(path: T; READONLY p: Point.T);

Extend`path`

with a linear segment that starts at its current point and ends at`p`

.

PROCEDURE CurveTo(path: T; READONLY q, r, s: Point.T);

Extend`path`

with a curved segment that starts at its current point and ends at`s`

.

`CurveTo`

adds a curve that starts from the current point of `path`

in the direction of `q`

, and ends at `s`

coming from the direction
of `r`

. More precisely, let `p`

be the current point of `path`

and let `h(t)`

and `v(t)`

be the cubic polynomials such that

(h(0), v(0)) = p (h(1), v(1)) = s (h'(0), v'(0)) = 3 * (q - p) (h'(1), v'(1)) = 3 * (s - r)(Where the primes denote differentiation with respect to

`t`

.) Then
`CurveTo`

adds the segment `(h(t), v(t))`

for `t`

between zero and
one. (This is called the {\it Bezier} arc determined by `p`

, `q`

,
`r`

, and `s`

.)
PROCEDURE Close(path: T);

More precisely, letAdd a linear segment to create a closed loop in`path`

.

`p`

be the current point of `path`

, and let
`q`

be last point of `path`

that was added by a call to `MoveTo`

(Thus `q`

is the startpoint of the first segment of the last subpath
of `path`

.) `Close`

adds a linear segment from `p`

to `q`

and marks
the sequence of segments from `q`

to the end of the path as a closed
subpath.
PROCEDURE IsEmpty(p: T): BOOLEAN;

Returns`TRUE`

if`p`

is empty.

PROCEDURE IsClosed(p: T): BOOLEAN;

Returns`TRUE`

if`p`

is empty or the last subpath of`p`

is closed.

PROCEDURE CurrentPoint(p: T): Point.T;

Returns the current point of`p`

.

`LineTo`

, `CurveTo`

, `Close`

, and `CurrentPoint`

are checked runtime
errors if the path has no current point.
EXCEPTION Malformed;The

`Malformed`

exception is raised when a procedure detects
a malformed path.
PROCEDURE Translate(p: T; READONLY delta: Point.T): T RAISES {Malformed};

The result of translating`p`

by`delta`

.

TYPE MapObject = OBJECT METHODS move(READONLY pt: Point.T); line(READONLY pt1, pt2: Point.T); close(READONLY pt1, pt2: Point.T); curve(READONLY pt1, pt2, pt3, pt4: Point.T) END; PROCEDURE Map(path: T; map: MapObject) RAISES {Malformed};

That is, for each segmentApply the appropriate method of`map`

to each segment of`path`

.

`s`

of `path`

, in order, `Map`

excecutes
the following:

IF sis a linear segment(p, q) THEN IF swas generated byMoveTo THEN (* p = q| map.move(p) | ELSIF s `was generated by` LineTo THEN | map.line(p, q) | ELSE (* s `was generated by` Close *) | map.close(p, q) | END | ELSE (* s `is a curved segment` (p, q, r, s) *) | map.curve(p, q, r, s) | END "Map" raises the exception if it is passed a malformed path. *) PROCEDURE Copy(p: T): T;Returns a newly allocated path with the same contents as`p`

.PROCEDURE Flatten(p: T): T RAISES {Malformed};Return a path like`p`

but with curved segments replaced by polygonal approximations.PROCEDURE BoundingBox(p: T): Rect.T RAISES {Malformed};Return a rectangle that contains all points of`p`

, and that is as small as convenient to compute.END Path.