Translate, rotate, scale

Easier than recomputing every point: move the grid itself and draw in it as if for the first time

mediumYou need: Shapes and lines, Angles and distances

A rectangle cannot be rotated by the rect command — it has no rotation field. But the grid itself it is drawn in can be rotated.

steptick 0

Draw0

clear

rgb

Draw1

color

rgb

a

Draw2

rect

xy

widthheight

Draw3

translate

xy

Draw4

rotate

degrees

Draw5

rect

xy

widthheight

Draw6

reset

Draw7

color

rgb

a

Draw8

rect

xy

widthheight

Draw Flush9

Stop10

@counter0number

Three squares are given identically, 40 by 40. The first is drawn as is, the second after the grid was moved and turned, the third after a reset, back in ordinary coordinates.

Three commands and an undo

Command	Fields	What it does
translate	x y	moves the origin
rotate	angle	turns the grid by an angle in degrees
scale	x y	stretches the grid along the axes
reset	—	puts everything back as it was

Rotation has only one field — the angle. In the text form it still stands third: draw rotate 0 0 90. The first two places are taken by coordinates this command does not use — that is how every draw is written, they share one set of fields.

They accumulate: a move after a move adds up, and so does a turn after a turn. Only reset undoes them.

Note

Scale is counted in steps of 0.05, and a one in that counting is 20:

draw scale	What you get
20 20	nothing changes
40 40	twice as big
10 10	half the size

The field is a whole number; there is no need to write fractions into it — the step size is already built in.

What it is for

There is no other way to rotate a shape: rect, line and triangle have no rotation at all, and poly has one, but only around its own centre. The grid solves both problems:

draw translate 88 88
draw rotate 0 0 angle
draw rect -20 -20 40 40
draw reset

The square is drawn around zero — from -20 to 20 — so the rotation turns it about its own middle, and translate puts that middle in the centre of the display. A compass needle, a clock’s second hand, a turning turret — all of them are built this way.

Silent failure

A forgotten reset spoils the next iteration. Transforms do not undo themselves: a program that does translate 88 88 every iteration and never cancels it draws past the edge of the display by the tenth one — and that looks like “the picture drifted off and vanished”.

The rule is simple: as many transforms as you set, that many resets — or better, one reset at the start of the iteration, right after clear.

Remember

• translate, rotate and scale change the coordinate system, not the shape.
• They accumulate, and only reset undoes them.
• Scale is counted in steps of 0.05.
• To make a shape spin about itself, draw it around zero and put it in place with a move.

Task

Change draw rotate 0 0 45 in the example to draw rotate 0 0 10 and run it: the second square almost straightens up.

Then remove the draw reset line: the third square — the blue one — drifts and turns as well, even though nothing changed in its own coordinates.