A first experiment with 2D soft bodies:
--
-- Fixed-Area Bubble in Lua for Codea
--
-- Based on E W Jordan's algorithm implemented in Processing
-- http://www.ewjordan.com/processing/VolumeBlob/ConstantAreaBlob.pde
-- Licence: Unknown
--
supportedOrientations(LANDSCAPE_ANY)
displayMode(FULLSCREEN)
function setup()
twoPi = 2 * math.pi
epsilon = .0001
g = 9.8 * 3 -- Gravity
l = 10 -- Left edge
r = WIDTH - 10 -- Right edge
b = 10 -- Bottom edge
t = HEIGHT - 10 -- Top edge
tRadius = 50 -- Size of touch circle
tX = WIDTH/4 -- Position of touch circle
tY = HEIGHT/4
tvX = 0 -- Velocity of touch circle
tvY = 0
k = 3 -- Spring strength
drag = 2 -- Drag on movement
destX = tX -- Destination of touch circle
destY = tY
jForce = 200 -- Strength of jump, if double-tapped
n = 40 -- Number of points in bubble
bRadius = 100 -- Size of bubble
nIters = 5
relax = 0.9
setupBubble() -- Create the bubble
textMode(CORNER)
end
function draw()
respondToEvents()
integrate(DeltaTime)
constrainEdges()
collideWithWalls()
collideWithTouch()
updateTouch(DeltaTime)
background(0)
fill(255)
text("Fixed-area Bubble (with acknowledgements to E W Jordan)",
10 , HEIGHT - 25)
drawBubble()
drawTouch()
end
function touched(touch)
if isInsideBubble(touch.x, touch.y) then
if touch.tapCount == 2 and touch.state == ENDED and
hitFloor then
jump = true
end
else
destX = touch.x
destY = touch.y
end
end
function isInsideBubble(pX, pY)
for i = 1, n do
local c = (pY - y[i]) * (x[i % n + 1] - x[i]) -
(pX - x[i]) * (y[i % n + 1] - y[i])
if c > 0 then return false end
end
return true
end
function updateTouch(dt)
local fX = (destX - tX) * k - tvX * drag
local fY = (destY - tY) * k - tvY * drag
tvX = tvX + fX * dt
tvY = tvY + fY * dt
tX = tX + tvX * dt
tY = tY + tvY * dt
end
function respondToEvents()
if jump and hitFloor then
local cmx = 0
local cmy = 0
for i = 1, n do
cmx = cmx + x[i]
cmy = cmy + y[i]
end
cmx = cmx / n
cmy = cmy / n
for i = 1, n do
ax[i] = ax[i] - (x[i] - cmx) * jForce
end
jump = false
end
end
function drawTouch()
stroke(0, 240, 255)
strokeWidth(5)
noFill()
ellipse(tX, tY, 2 * tRadius)
end
function drawBubble()
fill(255)
stroke(255)
strokeWidth(5)
for i = 1, n do
line(x[i], y[i], x[i % n + 1], y[i % n + 1])
end
end
function setupBubble()
x = {}
y = {}
xLast = {}
yLast = {}
ax = {}
ay = {}
local cx = WIDTH/2
local cy = HEIGHT/2
for i = 1, n do
local a = (i - 1)/n * twoPi
x[i] = cx + math.sin(a) * bRadius
y[i] = cy + math.cos(a) * bRadius
xLast[i] = x[i]
yLast[i] = y[i]
ax[i] = 0
ay[i] = 0
end
local dx = x[2] - x[1]
local dy = y[2] - y[1]
len = math.sqrt(dx * dx + dy * dy)
bubbleAreaTarget = bubbleArea()
end
function fixEdge()
local dx = {}
local dy = {}
for i = 1, n do
dx[i] = 0
dy[i] = 0
end
for count = 1, nIters do
for i = 1, n do
local j = i % n + 1
local eX = x[j] - x[i]
local eY = y[j] - y[i]
local d = math.sqrt(eX * eX + eY * eY)
if d < epsilon then d = 1 end
local ratio = 1 - len / d
dx[i] = dx[i] + relax * eX * ratio / 2
dy[i] = dy[i] + relax * eY * ratio / 2
dx[j] = dx[j] - relax * eX * ratio / 2
dy[j] = dy[j] - relax * eY * ratio / 2
end
for i = 1, n do
x[i] = x[i] + dx[i]
y[i] = y[i] + dy[i]
dx[i] = 0
dy[i] = 0
end
end
end
function constrainEdges()
fixEdge()
local edge = 0
local nx = {}
local ny = {}
for i = 1, n do
local j = i % n + 1
local dx = x[j] - x[i]
local dy = y[j] - y[i]
local d = math.sqrt(dx * dx + dy * dy)
if d < epsilon then d = 1 end
nx[i] = dy / d
ny[i] = -dx / d
edge = edge + d
end
local dArea = bubbleAreaTarget - bubbleArea()
local dH = 0.5 * dArea / edge
for i = 1, n do
local j = i % n + 1
x[j] = x[j] + dH * (nx[i] + nx[j])
y[j] = y[j] + dH * (ny[i] + ny[j])
end
end
function bubbleArea()
local area = 0
for i= 1, n do
area = area + x[i] * y[i % n + 1] - x[i % n + 1] * y[i]
end
area = area/2
return area
end
function integrate(dt)
local dtSqr = dt * dt
for i = 1, n do
local tempX = x[i]
local tempY = y[i]
x[i] = 2 * x[i] - xLast[i] + ax[i] * dtSqr
y[i] = 2 * y[i] - yLast[i] + ay[i] * dtSqr - g * dtSqr
xLast[i] = tempX
yLast[i] = tempY
ax[i] = 0
ay[i] = 0
end
end
function collideWithWalls()
hitFloor = false
for i = 1, n do
if x[i] < l then x[i] = l end
if x[i] > r then x[i] = r end
if y[i] < b then
y[i] = b
xLast[i] = x[i]
hitFloor = true
end
if y[i] > t then y[i] = t end
end
end
function collideWithTouch()
for i = 1, n do
local dx = tX - x[i]
local dy = tY - y[i]
local dSqr = dx * dx + dy * dy
if not (dSqr > tRadius*tRadius or
dSqr < epsilon * epsilon) then
local d = math.sqrt(dSqr)
x[i] = x[i] - dx * (tRadius/d - 1)
y[i] = y[i] - dy * (tRadius/d - 1)
end
end
end
