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$24(B-Spline Demonstrator

by Jeremy Gibbons)
$22(March 1987)
$b4

$b2$v5$22(Introduction)
$p1 This program is an interactive $30(B-spline) editor; it demonstrates
the use of quadratic B-splines for drawing curves. The curve can be
$30(open) or $30(closed). Multiple (double) knots can be placed 
in arbitrary positions. There is no restriction on the order of
adding, changing and removing $30(control points) and of making
$30(multiple knots). In addition, the $30(convex hull) of the curve
can be drawn.
$p0 The source and object files are $20(JG:Curve) and 
$20(JG:Curve.mob), respectively, on filestore C.

$b2$v5$22(Commands)
$p1 Interaction is entirely mouse driven. As well as the area of the screen
used to display the curve, there is a menu giving the available
commands, and a display of the $30(knot set) (see description of
how to make multiple knots). To select a command, the cursor is placed
on it, and any button is clicked.

$p0 To $30(change) (move) control points, the user moves the cursor over
the point in question, presses the left mouse button, moves the
point to the desired position, and then releases the mouse button.
The control polygon and the curve are continually redrawn to reflect
the position of the changing point. Several points can be changed; clicking
the right mouse button returns the cursor to the menu.

$p0 Points are $30(added) between two consecutive control points. Clicking
the left button moves a highlight round edges of the control polygon.
Pressing the middle button places a new control point in the middle of
this edge; the point can be repositioned as when changing points, above,
until the button is released.
Again, this can be repeated as often as desired; clicking the right
button returns the cursor to the menu.
The knot set is updated accordingly (adding a single knot).

$p0 To $30(remove) a point, the cursor is positioned over it and the
left button clicked. The point is removed, and the knot set is updated.
If there was a kink in the curve at that point, the double knot is made
single; if not, a knot is removed. Note that this may remove
a kink elsewhere (close by) in the curve. If every knot is a double
knot, there will only be a kink at every other control point. Removing
a control point at which there is no kink necessarily makes a double
knot single.
$p0 Care is taken not to remove the triple knots at the ends of an
open curve, otherwise the curve wouldn't terminate properly.
There is a minimum of three control points, whether the curve is open
or closed. Again, several points can be removed before returning to the
menu.

$p0 The knot set is displayed on a scale from 0 to N, the maximum knot
value; at each point on the scale, a dot is drawn for each of the knots
at that value. Thus, at the ends of an open curve (0 and N) there
are three dots; at double knots, two, and at single knots, one dot.
The cursor is moved up and down this scale to choose a point to
$30(make multiple). The left button is clicked on the required knot;
if it isn't already multiple, it is made so, and an extra control
point is added at that place on the curve (the kink in the curve
will be at this new control point). Clicking the right button
returns to the menu. Multiple knots are made single again by
removing the control point at the kink in the curve.

$p0 $30(Show convex hull) is a toggle; selecting it displays the
convex hull (and leaves the cursor on the menu). The command gets
replaced with the comand $30(Hide convex hull). Clicking on this removes
the convex hull. While it is displayed, the convex hull moves
with the curve.

$p0 $30(Initialise open curve) and $30(Initialise closed curve) set the
control polygon to a square. If the curve is open, it is a U-shape,
otherwise it is circular(ish).

$p0 $30(Quit) allows a clean exit from the program.

$b2$v5$22(Missing Features and Problems)
$p1 The curve is drawn using fixed point (ie, integers shifted up 8 places)
arithmetic for speed. I tried further optimisation in the form of a difference
technique to avoid the multiplications, but this seemed to make no
difference whatsoever.

$p0 Mouse debouncing is primitive. It consists of reading the mouse
buttons, then waiting for a while (fifty times round an empty loop).

$p0 When moving control points, a section of the curve gets erased and
redrawn. This occasionally erases other bits of the curve; this is cured
by redrawing the entire curve when the moved point is put down.
With better economy of planes (there is only one free plane at the moment),
moving sections could be drawn on different planes, avoiding this problem.

$p0 When a point is selected, the first point near (within nine pixels of)
the cursor is found. This occasionally means that a previous point is
picked up instead of the intended one. This can be cured by moving the
offending (previous) point, moving the desired point out from 
underneath it, then replacing the first point.

$p0 There is a bit of flicker when redrawing the curve while moving a point.
This is especially bad at the ends of the curve; the time taken to redraw
is perhaps close to (a multiple of) the time taken to refresh the display,
resulting in a "standing wave" effect. The flicker could be cured by
double buffering - drawing alternate images in different halves of the
framestore.

$p0 None of these problems reduces the programs's ability to perform
its task, which is to demonstrate quadratic B-spline curves.
$e