(Redirected from Bezier Curve)
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For more information, see Bézier curve on Wikipedia. A Bézier Curve is a smooth curve with many control points. It is infinitely scalable and often used in graphics and terrain generation. To make one in Scratch, one must use the following two methods:
Method 1
when green flag clicked hide pen up set pen size to (2) forever erase all def p-line :: custom set pen color to (#268435) draw p-line :: custom set pen color to (255) draw b-line steps: (90) :: custom end define set q-point A: (A.x :: custom-arg) (A.y :: custom-arg) B: (B.x :: custom-arg) (B.y :: custom-arg) progress: (progress :: custom-arg) set [q.x v] to ((A.x :: custom-arg) + ((progress :: custom-arg) * ((B.x :: custom-arg) - (A.x :: custom-arg)))) set [q.y v] to ((A.y :: custom-arg) + ((progress :: custom-arg) * ((B.y :: custom-arg) - (A.y :: custom-arg)))) define def p-line delete all of [p.x v] delete all of [p.y v] add ([x position v] of [P.00 v]) to [p.x v] // These are all the controls points of the curve, using clones is another solution to this. add ([y position v] of [P.00 v]) to [p.y v] add ([x position v] of [P.01 v]) to [p.x v] add ([y position v] of [P.01 v]) to [p.y v] add ([x position v] of [P.02 v]) to [p.x v] add ([y position v] of [P.02 v]) to [p.y v] add ([x position v] of [P.03 v]) to [p.x v] add ([y position v] of [P.03 v]) to [p.y v] add ([x position v] of [P.04 v]) to [p.x v] add ([y position v] of [P.04 v]) to [p.y v] add ([x position v] of [P.05 v]) to [p.x v] add ([y position v] of [P.05 v]) to [p.y v] add ([x position v] of [P.06 v]) to [p.x v] add ([y position v] of [P.06 v]) to [p.y v] add ([x position v] of [P.07 v]) to [p.x v] add ([y position v] of [P.07 v]) to [p.y v] add ([x position v] of [P.08 v]) to [p.x v] add ([y position v] of [P.08 v]) to [p.y v] add ([x position v] of [P.09 v]) to [p.x v] add ([y position v] of [P.09 v]) to [p.y v] add ([x position v] of [P.10 v]) to [p.x v] add ([y position v] of [P.10 v]) to [p.y v] add ([x position v] of [P.11 v]) to [p.x v] add ([y position v] of [P.11 v]) to [p.y v] add ([x position v] of [P.12 v]) to [p.x v] add ([y position v] of [P.12 v]) to [p.y v] add ([x position v] of [P.13 v]) to [p.x v] add ([y position v] of [P.13 v]) to [p.y v] define set b-point progress: (progress :: custom-arg) delete all of [b.x v] delete all of [b.y v] repeat (length of [p.x v]) add (item ((length of [b.x v]) + (1)) of [p.x v]) to [b.x v] add (item ((length of [b.y v]) + (1)) of [p.y v]) to [b.y v] end set [index.n v] to [1] repeat ((length of [b.x v]) - (index.n)) repeat ((length of [b.x v]) - (index.n)) set q-point A: (item (index.n) of [b.x v]) (item (index.n) of [b.y v]) B: (item ((index.n) + (1)) of [b.x v]) (item ((index.n) + (1)) of [b.y v]) progress: (progress :: custom-arg) :: custom add (q.x) to [b.x v] add (q.y) to [b.y v] change [index.n v] by (1) end change [index.n v] by (1) end define draw p-line set [loop.n v] to [1] go to x: (item (loop.n) of [p.x v]) y: (item (loop.n) of [p.y v]) pen down repeat ((length of [p.x v]) - (loop.n)) change [loop.n v] by (1) go to x: (item (loop.n) of [p.x v]) y: (item (loop.n) of [p.y v]) end pen up define draw b-line steps: (steps :: custom-arg) set [loop.n v] to [0] set b-point progress: ((loop.n) / (steps :: custom-arg)) :: custom go to x: (q.x) y: (q.y) pen down repeat ((steps :: custom-arg) - (loop.n)) change [loop.n v] by (1) set b-point progress: ((loop.n) / (steps :: custom-arg)) :: custom go to x: (q.x) y: (q.y) end pen up
Method 2
One sprite needs these scripts:
When green flag clicked hide delete all of [clone x v] delete all of [clone y v] set drag mode [draggable v] make clones define make clones set [Clone ID v] to (1) //local variable repeat (. . .:: grey) //the amount of points defining the curve create clone of (myself v) add () to [clone x v] add () to [clone y v] change [Clone ID v] by (1) end When I start as a clone show//make sure it has a costume go to (random position v) forever replace item (clone ID) of [clone x v] with (x position) replace item (clone ID) of [clone y v] with (y position) end
In another sprite, insert these scripts:
when green flag clicked forever erase all draw line between dots//without screen refresh find curve points//without screen refresh end define copy main points delete all of [x v] delete all of [y v] set [counter v] to (1) repeat (length of [clone x v]) add (item (counter) of [clone x v]) to [x v] add (item (counter) of [clone y v]) to [y v] change [counter v] by (1) end define find curve points delete all of [curve x v] delete all of [curve y v] set [t v] to (1) repeat (100) copy main points // copies the "x" and "y" lists to "clone x" and "clone y" respectively repeat until <(length of [x v]) = (1)> find lines end add (x:: list) to [curve x v] add (y:: list) to [curve y v] change [t v] by (1) end draw curve define move (t)% to x: (x) y: (y) point in direction (([atan v] of (((x position)-(x))/((y position)-(y))))+((180)*<(y position)<(y)>)) move (([sqrt v] of ((((x position)-(x))*((x position)-(x)))+(((y position)-(y))*((y position)-(y)))))*((t)/(100))) steps define find lines set [line counter v] to (1) repeat ((length of [x v])-(1)) go to x: (item (line counter) of [x v]) y: (item (line counter) of [y v]) move (t)% to x: (item ((line counter)+(1)) of [x v]) y: (item ((line counter)+(1)) of [y v]) add (x position) to [x v] add (y position) to [y v] change [line counter v] by (1) end repeat ((line counter)-(1)) delete (1) of [x v] delete (1) of [y v] end define draw curve go to x: (item (1) of [curve x v]) y: (item (1) of [curve y v]) pen down set [line counter v] to (1) repeat (length of [curve x v]) go to x: (item (line counter) of [curve x v]) y: (item (line counter) of [curve y v]) change [line counter v] by (1) end pen up define draw line between dots go to x: (item (1) of [clone x v]) y: (item (1) of [clone y v]) pen down set [line counter v] to (1) repeat (length of [clone x v]) go to x: (item (line counter) of [clone x v]) y: (item (line counter) of [clone y v]) change [line counter v] by (1) end pen up
Uses of Bézier Curves
There are many uses of Bézier curves within Scratch. These can include:
- Combining them with velocity to make things fall or bounce.
- Rendering a terrain with hills so that when one zooms in, the curve still looks nice.
- Making customisable graphs.