[DBP] 3D Bezier Curve - GameCreators Forum

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MonoCoder

18

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Joined: 4th Dec 2005

Location: england

Posted: 25th Aug 2010 22:57 Edited at: 25th Aug 2010 23:02

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Probably bindun, but I'm learning it at the moment so figured I'd share. Currently very sloppy code, but it works and I'll call back a few times to fix it up and add features and things to it. Uses Matrix1Utils, but you can get round having to use it by getting rid of the "random(?)" bits and replacing them with "(rnd(?*10.0)/10.0)" or something.

Move mouse to orbit camera, scroll mousewheel to zoom in/out. Press control to re-randomize the points, hold shift to slide the middle point along x/y (quick and easy visualisation aid-y thing), or hold space to watch the bezier being traced. Lower cBezierSamples to make the curve less smooth/faster to draw, and vice versa.

set display mode desktop width(), desktop height(), 32, 1
sync on
sync rate 60

#constant cBezierSamples 50.0

type tInputKey
	Old
	New
endtype

type tVec3D
	x as float
	y as float
	z as float
endtype
type tBezierPoint
	pos as tVec3D
	handleprev as tVec3D
	handlenext as tVec3D
endtype
type tBezierLineThree
	start as tBezierPoint
	mid as tBezierPoint
	last as tBezierPoint
endtype

global gBezier as tBezierLineThree
global Bezier as tBezierLineThree
global gCtrl as tInputKey

// Make Bezier Handles.
for a = 1 to 3
	make object cube ((a - 1) * 3) + 1, 2
	make object cube ((a - 1) * 3) + 2, 1
	make object cube ((a - 1) * 3) + 3, 1
next a
// Make Temp Object.
make object cube 100, 1
`hide object 100

BezierRnd(100.0)
gBezier = Bezier
UpdateBezier()

do

// update input.
	gCtrl.Old = gCtrl.New
	gCtrl.New = controlkey()

if gCtrl.New
		if gCtrl.Old = 0
			// Randomize Bezier Line
			BezierRnd(100.0)
			gBezier = Bezier
			UpdateBezier()
		endif
	endif
	
	if shiftkey()
		inc gBezier.Mid.Pos.X, 0.1
		inc gBezier.Mid.Pos.Y, 0.1
		UpdateBezier()
	endif
	
	// Update camera.
	rotate camera camera angle x() + mousemovey(), camera angle y() + mousemovex(), 0
	position camera 0, 0, 0
	move camera -384 + (mousez()/10.0)

// Draw Non-Bezier Line
	startx = object screen x(1)
	starty = object screen y(1)
	midx = object screen x(4)
	midy = object screen y(4)
	lastx = object screen x(7)
	lasty = object screen y(7)
	ink rgb(255, 255, 255)
	line startx, starty, midx, midy
	line midx, midy, lastx, lasty
	
	// DRAW 3D BEZIER.
	// We draw two bezier curves: The curve Start-Mid, and the curve Mid-Last.
	ink rgb(255, 0, 255)
	DrawBezier(gBezier.Start, gBezier.Mid)
	DrawBezier(gBezier.Mid, gBezier.Last)
	
	// Draw Handles
	starthandleprevx = object screen x(2)
	starthandleprevy = object screen y(2)
	starthandlenextx = object screen x(3)
	starthandlenexty = object screen y(3)
	midhandleprevx = object screen x(5)
	midhandleprevy = object screen y(5)
	midhandlenextx = object screen x(6)
	midhandlenexty = object screen y(6)
	lasthandleprevx = object screen x(8)
	lasthandleprevy = object screen y(8)
	lasthandlenextx = object screen x(9)
	lasthandlenexty = object screen y(9)
	ink rgb(0, 0, 245)
	line startx, starty, starthandleprevx, starthandleprevy
	line startx, starty, starthandlenextx, starthandlenexty
	line midx, midy, midhandleprevx, midhandleprevy
	line midx, midy, midhandlenextx, midhandlenexty
	line lastx, lasty, lasthandleprevx, lasthandleprevy
	line lastx, lasty, lasthandlenextx, lasthandlenexty
	
	set cursor 0, 0
	ink rgb(255, 255, 255)
	print screen fps()
	
sync
loop

function BezierRnd(PosRndMax)
	Bezier.Start.Pos.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.Pos.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.Pos.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandlePrev.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandlePrev.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandlePrev.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandleNext.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandleNext.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandleNext.Z = -(PosRndMax / 2) + (random(PosRndMax))
	
	Bezier.Mid.Pos.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.Pos.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.Pos.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandlePrev.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandlePrev.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandlePrev.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandleNext.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandleNext.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandleNext.Z = -(PosRndMax / 2) + (random(PosRndMax))
	
	Bezier.Last.Pos.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.Pos.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.Pos.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandlePrev.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandlePrev.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandlePrev.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandleNext.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandleNext.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandleNext.Z = -(PosRndMax / 2) + (random(PosRndMax))
endfunction

function UpdateBezier()
	position object 1, gBezier.Start.Pos.X, gBezier.Start.Pos.Y, gBezier.Start.Pos.Z
	position object 4, gBezier.Mid.Pos.X, gBezier.Mid.Pos.Y, gBezier.Mid.Pos.Z
	position object 7, gBezier.Last.Pos.X, gBezier.Last.Pos.Y, gBezier.Last.Pos.Z
	position object 2, gBezier.Start.HandlePrev.X, gBezier.Start.HandlePrev.Y, gBezier.Start.HandlePrev.Z
	position object 5, gBezier.Mid.HandlePrev.X, gBezier.Mid.HandlePrev.Y, gBezier.Mid.HandlePrev.Z
	position object 8, gBezier.Last.HandlePrev.X, gBezier.Last.HandlePrev.Y, gBezier.Last.HandlePrev.Z
	position object 3, gBezier.Start.HandleNext.X, gBezier.Start.HandleNext.Y, gBezier.Start.HandleNext.Z
	position object 6, gBezier.Mid.HandleNext.X, gBezier.Mid.HandleNext.Y, gBezier.Mid.HandleNext.Z
	position object 9, gBezier.Last.HandleNext.X, gBezier.Last.HandleNext.Y, gBezier.Last.HandleNext.Z
endfunction

function DrawBezier(A as tBezierPoint, B as tBezierPoint)
	local AHandlePos as tVec3D
	local BHandlePos as tVec3D
	
	ax as float : ay as float : az as float
	bx as float : by as float : bz as float
	cx as float : cy as float : cz as float
	
	
	local drawxold = 0
	local drawyold = 0
	position object 100, A.Pos.X, A.Pos.Y, A.Pos.Z
	local drawxnew : drawxnew = object screen x(100)
	local drawynew : drawynew = object screen y(100)
	`backdrop off
	
	for t = 0 to cBezierSamples
		// Get Position along the Next Handle of A.
		ax = ((A.HandleNext.X - A.Pos.X) / cBezierSamples) * (t*1.0) + A.Pos.X
		ay = ((A.HandleNext.Y - A.Pos.Y) / cBezierSamples) * (t*1.0) + A.Pos.Y
		az = ((A.HandleNext.Z - A.Pos.Z) / cBezierSamples) * (t*1.0) + A.Pos.Z
		
		// Get Position along the Prev Handle of B.
		bx = ((B.HandlePrev.X - B.Pos.X) / cBezierSamples) * ((cBezierSamples-t)*1.0) + B.Pos.X
		by = ((B.HandlePrev.Y - B.Pos.Y) / cBezierSamples) * ((cBezierSamples-t)*1.0) + B.Pos.Y
		bz = ((B.HandlePrev.Z - B.Pos.Z) / cBezierSamples) * ((cBezierSamples-t)*1.0) + B.Pos.Z
		
		// Get Position along the Line ax,ay,az - bx,by,bz.
		cx = ((bx - ax) / cBezierSamples) * (t*1.0) + ax
		cy = ((by - ay) / cBezierSamples) * (t*1.0) + ay
		cz = ((bz - az) / cBezierSamples) * (t*1.0) + az
		
		position object 100, cx, cy, cz
		drawxold = drawxnew
		drawyold = drawynew
		drawxnew = object screen x(100)
		drawynew = object screen y(100)
		
		// Draw Bezier Curve Section.
		line drawxold, drawyold, drawxnew, drawynew
		
		f = f + 1 : if f = 4 and spacekey() then sync : f = 0
		
	next t
	`backdrop on
endfunction

+ Code Snippet

set display mode desktop width(), desktop height(), 32, 1
sync on
sync rate 60

#constant cBezierSamples 50.0

type tInputKey
	Old
	New
endtype

type tVec3D
	x as float
	y as float
	z as float
endtype
type tBezierPoint
	pos as tVec3D
	handleprev as tVec3D
	handlenext as tVec3D
endtype
type tBezierLineThree
	start as tBezierPoint
	mid as tBezierPoint
	last as tBezierPoint
endtype

global gBezier as tBezierLineThree
global Bezier as tBezierLineThree
global gCtrl as tInputKey

// Make Bezier Handles.
for a = 1 to 3
	make object cube ((a - 1) * 3) + 1, 2
	make object cube ((a - 1) * 3) + 2, 1
	make object cube ((a - 1) * 3) + 3, 1
next a
// Make Temp Object.
make object cube 100, 1
`hide object 100

BezierRnd(100.0)
gBezier = Bezier
UpdateBezier()


do

	// update input.
	gCtrl.Old = gCtrl.New
	gCtrl.New = controlkey()

	if gCtrl.New
		if gCtrl.Old = 0
			// Randomize Bezier Line
			BezierRnd(100.0)
			gBezier = Bezier
			UpdateBezier()
		endif
	endif
	
	if shiftkey()
		inc gBezier.Mid.Pos.X, 0.1
		inc gBezier.Mid.Pos.Y, 0.1
		UpdateBezier()
	endif
	
	// Update camera.
	rotate camera camera angle x() + mousemovey(), camera angle y() + mousemovex(), 0
	position camera 0, 0, 0
	move camera -384 + (mousez()/10.0)

	// Draw Non-Bezier Line
	startx = object screen x(1)
	starty = object screen y(1)
	midx = object screen x(4)
	midy = object screen y(4)
	lastx = object screen x(7)
	lasty = object screen y(7)
	ink rgb(255, 255, 255)
	line startx, starty, midx, midy
	line midx, midy, lastx, lasty
	
	// DRAW 3D BEZIER.
	// We draw two bezier curves: The curve Start-Mid, and the curve Mid-Last.
	ink rgb(255, 0, 255)
	DrawBezier(gBezier.Start, gBezier.Mid)
	DrawBezier(gBezier.Mid, gBezier.Last)
	
	// Draw Handles
	starthandleprevx = object screen x(2)
	starthandleprevy = object screen y(2)
	starthandlenextx = object screen x(3)
	starthandlenexty = object screen y(3)
	midhandleprevx = object screen x(5)
	midhandleprevy = object screen y(5)
	midhandlenextx = object screen x(6)
	midhandlenexty = object screen y(6)
	lasthandleprevx = object screen x(8)
	lasthandleprevy = object screen y(8)
	lasthandlenextx = object screen x(9)
	lasthandlenexty = object screen y(9)
	ink rgb(0, 0, 245)
	line startx, starty, starthandleprevx, starthandleprevy
	line startx, starty, starthandlenextx, starthandlenexty
	line midx, midy, midhandleprevx, midhandleprevy
	line midx, midy, midhandlenextx, midhandlenexty
	line lastx, lasty, lasthandleprevx, lasthandleprevy
	line lastx, lasty, lasthandlenextx, lasthandlenexty
	
	set cursor 0, 0
	ink rgb(255, 255, 255)
	print screen fps()
	
sync
loop



function BezierRnd(PosRndMax)
	Bezier.Start.Pos.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.Pos.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.Pos.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandlePrev.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandlePrev.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandlePrev.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandleNext.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandleNext.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Start.HandleNext.Z = -(PosRndMax / 2) + (random(PosRndMax))
	
	Bezier.Mid.Pos.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.Pos.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.Pos.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandlePrev.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandlePrev.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandlePrev.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandleNext.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandleNext.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Mid.HandleNext.Z = -(PosRndMax / 2) + (random(PosRndMax))
	
	Bezier.Last.Pos.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.Pos.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.Pos.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandlePrev.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandlePrev.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandlePrev.Z = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandleNext.X = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandleNext.Y = -(PosRndMax / 2) + (random(PosRndMax))
	Bezier.Last.HandleNext.Z = -(PosRndMax / 2) + (random(PosRndMax))
endfunction



function UpdateBezier()
	position object 1, gBezier.Start.Pos.X, gBezier.Start.Pos.Y, gBezier.Start.Pos.Z
	position object 4, gBezier.Mid.Pos.X, gBezier.Mid.Pos.Y, gBezier.Mid.Pos.Z
	position object 7, gBezier.Last.Pos.X, gBezier.Last.Pos.Y, gBezier.Last.Pos.Z
	position object 2, gBezier.Start.HandlePrev.X, gBezier.Start.HandlePrev.Y, gBezier.Start.HandlePrev.Z
	position object 5, gBezier.Mid.HandlePrev.X, gBezier.Mid.HandlePrev.Y, gBezier.Mid.HandlePrev.Z
	position object 8, gBezier.Last.HandlePrev.X, gBezier.Last.HandlePrev.Y, gBezier.Last.HandlePrev.Z
	position object 3, gBezier.Start.HandleNext.X, gBezier.Start.HandleNext.Y, gBezier.Start.HandleNext.Z
	position object 6, gBezier.Mid.HandleNext.X, gBezier.Mid.HandleNext.Y, gBezier.Mid.HandleNext.Z
	position object 9, gBezier.Last.HandleNext.X, gBezier.Last.HandleNext.Y, gBezier.Last.HandleNext.Z
endfunction



function DrawBezier(A as tBezierPoint, B as tBezierPoint)
	local AHandlePos as tVec3D
	local BHandlePos as tVec3D
	
	ax as float : ay as float : az as float
	bx as float : by as float : bz as float
	cx as float : cy as float : cz as float
	
	
	local drawxold = 0
	local drawyold = 0
	position object 100, A.Pos.X, A.Pos.Y, A.Pos.Z
	local drawxnew : drawxnew = object screen x(100)
	local drawynew : drawynew = object screen y(100)
	`backdrop off
	
	for t = 0 to cBezierSamples
		// Get Position along the Next Handle of A.
		ax = ((A.HandleNext.X - A.Pos.X) / cBezierSamples) * (t*1.0) + A.Pos.X
		ay = ((A.HandleNext.Y - A.Pos.Y) / cBezierSamples) * (t*1.0) + A.Pos.Y
		az = ((A.HandleNext.Z - A.Pos.Z) / cBezierSamples) * (t*1.0) + A.Pos.Z
		
		// Get Position along the Prev Handle of B.
		bx = ((B.HandlePrev.X - B.Pos.X) / cBezierSamples) * ((cBezierSamples-t)*1.0) + B.Pos.X
		by = ((B.HandlePrev.Y - B.Pos.Y) / cBezierSamples) * ((cBezierSamples-t)*1.0) + B.Pos.Y
		bz = ((B.HandlePrev.Z - B.Pos.Z) / cBezierSamples) * ((cBezierSamples-t)*1.0) + B.Pos.Z
		
		// Get Position along the Line ax,ay,az - bx,by,bz.
		cx = ((bx - ax) / cBezierSamples) * (t*1.0) + ax
		cy = ((by - ay) / cBezierSamples) * (t*1.0) + ay
		cz = ((bz - az) / cBezierSamples) * (t*1.0) + az
		
		position object 100, cx, cy, cz
		drawxold = drawxnew
		drawyold = drawynew
		drawxnew = object screen x(100)
		drawynew = object screen y(100)
		
		// Draw Bezier Curve Section.
		line drawxold, drawyold, drawxnew, drawynew
		
		f = f + 1 : if f = 4 and spacekey() then sync : f = 0
		
	next t
	`backdrop on
endfunction

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Sixty Squares

17

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Joined: 7th Jun 2006

Location: Somewhere in the world

Posted: 27th Aug 2010 17:30

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Interesting snippet

. If you expanded on it you might be able to make a pretty cool screen saver.

Guns, cinematics, stealth, items and more!

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Neuro Fuzzy

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Joined: 11th Jun 2007

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Posted: 28th Aug 2010 11:30 Edited at: 21st Mar 2011 06:45

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[edit] nm O_o

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maggiemiller

13

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Joined: 24th Sep 2010

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Posted: 24th Sep 2010 09:38

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They are really nice information from you, I think a Bezier curve is a parametric curve often used in computer graphics and related fields, well, I think the 3D surface patches Bezier, they are defined by the network of 16 control points (4 rows 4 columns). Each row of four control points can be seen as a separate 2D Bezier curve.

document translation

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Code Snippets / [DBP] 3D Bezier Curve