require "physics" require "color"
function pV(x, y) return physics.Vect(x, y) end
function sum(list) local result = ZERO for _, v in ipairs(list) do result = result + v end return result end
function centroid(vertsList) local numVerts = #vertsList/2 local points = vertsList points[#points+1] = vertsList[1] points[#points+1] = vertsList[2] local x, y = {}, {} for i = 1, #points/2 do x[i], y[i] = points[2*i-1], points[2*i] end local xc, yc, eachAreas = {}, {}, {} local totalArea, xgTemp, ygTemp = 0, 0, 0 for i = 1, numVerts do xc[i], yc[i] = (x[i] + x[i+1])/3, (y[i] + y[i+1])/3 eachAreas[i] = (x[i+1] * y[i] - y[i+1] * x[i])/2 totalArea = totalArea + eachAreas[i] xgTemp, ygTemp = xgTemp + eachAreas[i] * xc[i], ygTemp + eachAreas[i] * yc[i] end return xgTemp/totalArea, ygTemp/totalArea; end
function compCentroid(vertsMat) function centroid2(vertsList) local numVerts = #vertsList/2 local points = vertsList points[#points+1] = vertsList[1] points[#points+1] = vertsList[2] local x, y = {}, {} for i = 1, #points/2 do x[i], y[i] = points[2*i-1], points[2*i] end local xc, yc, eachAreas = {}, {}, {} local totalArea, xgTemp, ygTemp = 0, 0, 0 for i = 1, numVerts do xc[i], yc[i] = (x[i] + x[i+1])/3, (y[i] + y[i+1])/3 eachAreas[i] = (x[i+1] * y[i] - y[i+1] * x[i])/2 totalArea = totalArea + eachAreas[i] xgTemp, ygTemp = xgTemp + eachAreas[i] * xc[i], ygTemp + eachAreas[i] * yc[i] end return xgTemp/totalArea, ygTemp/totalArea, totalArea end local xg, yg, area = {}, {}, {} for i, v in ipairs(vertsMat) do xg[i], yg[i], area[i] = centroid2(v) end local tempXg, tempYg, totalArea = 0, 0, 0 for i = 1, #xg do tempXg, tempYg = tempXg + xg[i] * area[i], tempYg + yg[i] * area[i] totalArea = totalArea + area[i] end return tempXg/totalArea, tempYg/totalArea; end
function on.resize()
W, H = platform.window:width(), platform.window:height()
X0, Y0, UNIT = W/2, H/2, math.floor(W/60)
end
platform.window:setBackgroundColor(color.white)
TICKING = false
GRID = true
drawShape = false
drawHistory, maxHistory, penHistory = true, 100, "thin"
spaceDamping = nil
VLimit = nil
ZERO = pV(0, 0)
LARGE = physics.misc.INFINITY()
dtLua = 1/(2^6)
dtChipmunk = 1/(2^6)
GRAVITY = -10
COLOR = {
0xFF7F7F, 0xFF7FBF, 0xFF7FFF, 0xBF7FFF, 0x7F7FFF, 0x7FBFFF, 0x7FFFFF, 0x7FFFBF, 0x7FFF7F, 0xBFFF7F, 0xFFFF7F, 0xFFBF7F,
0xFF6060, 0xFF60AF, 0xFF60FF, 0xAF60FF, 0x6060FF, 0x60AFFF, 0x60FFFF, 0x60FFAF, 0x60FF60, 0xAFFF60, 0xFFFF60, 0xFFAF60,
0x5E5E5E, 0x7E7E7E, 0x9E9E9E, 0xBEBEBE, 0xDEDEDE,
0x0078BA, 0x0079C2, 0x009944, 0x00A0DE, 0x00A7DB, 0x00ADA9, 0x019A66, 0x522886, 0x6CBB5A, 0x814721, 0x9B7CB6, 0x9CAEB7, 0xA9CC51, 0xB6007A, 0xBB641D, 0xD7C447, 0xE44D93, 0xE5171F, 0xE60012, 0xE85298, 0xEE7B1A, 0xF39700,
}
pBall = class()
function pBall:init(mass, radius, elasticity, friction, color, group)
self.color = color
self.history = {}
local inertia = physics.misc.momentForCircle(mass, 0, radius, ZERO)
self.body = physics.Body(mass, inertia)
if VLimit then self.body:setVLimit(VLimit) end
self.shape = physics.CircleShape(self.body, radius, ZERO)
:setRestitution(elasticity)
:setFriction(friction)
if group then self.shape:setGroup(group) end
end
function pBall:paint(gc)
local pos = self.body:pos()
local cx, cy = X0 + UNIT * pos:x(), Y0 - UNIT * pos:y()
local radius = UNIT * self.shape:radius()
local diameter = radius + radius
local angle = self.body:angle()
local x0, y0 = cx - radius, cy - radius
gc:setColorRGB(self.color)
if drawHistory then
gc:setPen(penHistory)
self.history[#self.history+1] = cx
self.history[#self.history+1] = cy
if #self.history > maxHistory then table.remove(self.history, 1) table.remove(self.history, 1) end
gc:drawPolyLine(self.history)
end
gc:fillArc(x0, y0, diameter, diameter, 0, 360)
gc:setPen("thin")
gc:setColorRGB(color.black)
if drawShape then
gc:drawArc(x0, y0, diameter, diameter, 0, 360)
gc:drawLine(cx, cy, cx + radius * math.cos(angle), cy - radius * math.sin(angle))
end
end
pBox = class()
function pBox:init(mass, width, height, elasticity, friction, color, group)
self.color = color
self.history = {}
local inertia = physics.misc.momentForBox(mass, width, height)
self.body = physics.Body(mass, inertia)
if VLimit then self.body:setVLimit(VLimit) end
local verts = {pV(-width/2, -height/2), pV(-width/2, height/2), pV(width/2, height/2), pV(width/2, -height/2)}
self.shape = physics.PolyShape(self.body, verts, ZERO)
:setRestitution(elasticity)
:setFriction(friction)
if group then self.shape:setGroup(group) end
end
function pBox:paint(gc)
gc:setColorRGB(self.color)
if drawHistory then
gc:setPen(penHistory)
local pos = self.body:pos()
local cx, cy = X0 + UNIT * pos:x(), Y0 - UNIT * pos:y()
self.history[#self.history+1] = cx
self.history[#self.history+1] = cy
if #self.history > maxHistory then table.remove(self.history, 1) table.remove(self.history, 1) end
gc:drawPolyLine(self.history)
end
local numVerts = self.shape:numVerts()
local verts = {}
local points = self.shape:points()
for i = 1, numVerts do
verts[#verts+1] = X0 + UNIT * points[i]:x()
verts[#verts+1] = Y0 - UNIT * points[i]:y()
end
verts[#verts+1] = X0 + UNIT * points[1]:x()
verts[#verts+1] = Y0 - UNIT * points[1]:y()
gc:setPen("thin")
gc:fillPolygon(verts)
if drawShape then
gc:setColorRGB(color.black)
gc:drawPolyLine(verts)
end
end
pRegPoly = class(pBox)
function pRegPoly:init(mass, radius, numVerts, elasticity, friction, color, group)
self.color = color
self.history = {}
local unitAngle = 2 * math.pi/numVerts
local verts = {pV(radius, 0)}
for i = 1, numVerts - 1 do
verts[#verts+1] = pV(radius * math.cos(unitAngle * i), -radius * math.sin(unitAngle * i))
end
local inertia = physics.misc.momentForPoly(mass, verts, ZERO)
self.body = physics.Body(mass, inertia)
if VLimit then self.body:setVLimit(VLimit) end
self.shape = physics.PolyShape(self.body, verts, ZERO)
:setRestitution(elasticity)
:setFriction(friction)
if group then self.shape:setGroup(group) end
end
pIrregPoly = class(pBox)
function pIrregPoly:init(mass, vertsList, elasticity, friction, color, group)
self.color = color
self.history = {}
local offsetX, offsetY = centroid(vertsList)
local verts = {}
for i = 1, #vertsList/2 do
verts[i] = physics.Vect(vertsList[2*i-1] - offsetX, vertsList[2*i] - offsetY)
end
local inertia = physics.misc.momentForPoly(mass, verts, ZERO)
self.body = physics.Body(mass, inertia)
if VLimit then self.body:setVLimit(VLimit) end
self.shape = physics.PolyShape(self.body, verts, ZERO)
:setRestitution(elasticity)
:setFriction(friction)
if group then self.shape:setGroup(group) end
end
pCompPoly = class()
function pCompPoly:init(mass, vertsMat, outersList, elasticity, friction, color, group)
self.color = color
self.history = {}
local offsetX, offsetY = compCentroid(vertsMat)
local outersVect = {}
for i = 1, #outersList/2 do
outersVect[i] = physics.Vect(outersList[2*i-1] - offsetX, outersList[2*i] - offsetY)
end
local verts = {}
for i = 1, #vertsMat do
verts[i] = {}
for j = 1, #vertsMat[i]/2 do
verts[i][j] = physics.Vect(vertsMat[i][2*j-1] - offsetX, vertsMat[i][2*j] - offsetY)
end
end
local inertia = physics.misc.momentForPoly(mass, outersVect, ZERO)
self.body = physics.Body(mass, inertia)
if VLimit then self.body:setVLimit(VLimit) end
self.shapesList = {}
for i = 1, #vertsMat do
self.shapesList[i] = physics.PolyShape(self.body, verts[i], ZERO)
:setRestitution(elasticity)
:setFriction(friction)
if group then self.shapesList[i]:setGroup(group) end
end
end
function pCompPoly:paint(gc)
gc:setColorRGB(self.color)
if drawHistory then
gc:setPen(penHistory)
local pos = self.body:pos()
local cx, cy = X0 + UNIT * pos:x(), Y0 - UNIT * pos:y()
self.history[#self.history+1] = cx
self.history[#self.history+1] = cy
if #self.history > maxHistory then table.remove(self.history, 1) table.remove(self.history, 1) end
gc:drawPolyLine(self.history)
end
local points = {}
local verts = {}
local numShepes = #self.shapesList
gc:setPen("thin")
for i = 1, numShepes do
verts[i] = {}
points = self.shapesList[i]:points()
for j = 1, self.shapesList[i]:numVerts() do
verts[i][#verts[i]+1] = X0 + UNIT * points[j]:x()
verts[i][#verts[i]+1] = Y0 - UNIT * points[j]:y()
end
verts[i][#verts[i]+1] = X0 + UNIT * points[1]:x()
verts[i][#verts[i]+1] = Y0 - UNIT * points[1]:y()
end
for _, v in ipairs(verts) do
gc:fillPolygon(v)
end
if drawShape then
gc:setColorRGB(color.black)
for _, v in ipairs(verts) do
gc:drawPolyLine(v)
end
end
end
pStaticSeg = class()
function pStaticSeg:init(x1, y1, x2, y2, radius, elasticity, friction, color, group)
self.color = color
local avec, bvec = pV(x1, y1), pV(x2, y2)
self.shape = physics.SegmentShape(nil, avec, bvec, radius)
:setRestitution(elasticity)
:setFriction(friction)
if group then self.shape:setGroup(group) end
end
function pStaticSeg:paint(gc)
local pos1 = self.shape:a()
local x1, y1 = X0 + UNIT * pos1:x(), Y0 - UNIT * pos1:y()
local pos2 = self.shape:b()
local x2, y2 = X0 + UNIT * pos2:x(), Y0 - UNIT * pos2:y()
gc:setColorRGB(self.color)
gc:setPen("thick")
gc:drawLine(x1, y1, x2, y2)
end
pSpace = class()
function pSpace:init(GRAVITY)
self.space = physics.Space()
:setGravity(pV(0, GRAVITY))
if spaceDamping then self.space:setDamping(spaceDamping) end
self.objects = {}
end
function pSpace:step(DT)
self.space:step(DT)
end
function pSpace:addObj(obj, velx, vely, cx, cy)
obj.body:setVel(pV(velx, vely))
:setPos(pV(cx, cy))
self.space:addBody(obj.body)
:addShape(obj.shape)
self.objects[#self.objects+1] = obj
end
function pSpace:addCompPoly(obj, velx, vely, cx, cy)
obj.body:setVel(pV(velx, vely))
:setPos(pV(cx, cy))
self.space:addBody(obj.body)
for _, v in ipairs(obj.shapesList) do
self.space:addShape(v)
end
self.objects[#self.objects+1] = obj
end
function pSpace:addStatic(obj, cx, cy)
if obj.body then obj.body:setPos(pV(cx, cy)) end
self.space:addStaticShape(obj.shape)
self.objects[#self.objects+1] = obj
end
function pSpace:attractBetween()
local forceTable = {}
for r = 1, #self.objects do
forceTable[r] = {}
for c = 1, #self.objects do
if r == c then
forceTable[r][c] = ZERO
elseif r > c then
forceTable[r][c] = -forceTable[c][r]
else
local posA = self.objects[r].body:pos()
local posB = self.objects[c].body:pos()
local massA = self.objects[r].body:mass()
local massB = self.objects[c].body:mass()
local vectAB = posB - posA
local lengthABsq = vectAB:lengthsq()
local normAB = vectAB:normalize()
forceTable[r][c] = normAB:mult(massA * massB/lengthABsq)
end
end
self.objects[r].body:setForce(sum(forceTable[r]))
end
end
function pSpace:paint(gc)
gc:setColorRGB(color.gray)
if GRAVITY ~= 0 then gc:drawString(string.format("acceleration of gravity: %3.1f", GRAVITY), 5, -3, "top") end
if TICKING == true then gc:drawString("running", W - 70, 12, "top") end
if TICKING == false then gc:drawString("stopped", W - 70, 12, "top") end
gc:drawString(string.format("t = %4.1f", timeElapsed), W - 70, -3, "top")
for _, v in ipairs(self.objects) do
v:paint(gc)
end
end
function grid(gc)
gc:setPen("thin")
gc:setColorRGB(0x6495ED)
gc:drawLine(0, Y0, W, Y0)
gc:drawLine(X0, 0, X0, H)
gc:fillPolygon({W, Y0, W - 7, Y0 - 4, W - 3, Y0, W - 7, Y0 + 4, W, Y0})
gc:fillPolygon({X0, 0, X0 - 4, 7, X0, 3, X0 + 4, 7, X0, 0})
gc:setColorRGB(0xCAE1FF)
local i1 = 1; while Y0 - UNIT * i1 > 0 do gc:drawLine(0, Y0 - UNIT * i1, W, Y0 - UNIT * i1); i1 = i1 + 1 end
local i2 = 1; while Y0 + UNIT * i2 < H do gc:drawLine(0, Y0 + UNIT * i2, W, Y0 + UNIT * i2); i2 = i2 + 1 end
local i3 = 1; while X0 + UNIT * i3 < W do gc:drawLine(X0 + UNIT * i3, 0, X0 + UNIT * i3, H); i3 = i3 + 1 end
local i4 = 1; while X0 - UNIT * i4 > 0 do gc:drawLine(X0 - UNIT * i4, 0, X0 - UNIT * i4, H); i4 = i4 + 1 end
gc:setColorRGB(0x6495ED)
gc:drawString("x", W - 10, Y0 - 21)
gc:drawString("y", X0 + 5, -6)
end
function fence(x1, y1, x2, y2, radius, elasticity, friction)
local color = color.black
local a1, a2, a3, a4 = ((x1 - UNIT * radius) - X0)/UNIT, (Y0 - (y1 - UNIT * radius))/UNIT, (Y0 - (y2 + UNIT * radius))/UNIT, ((x2 + UNIT * radius) - X0)/UNIT
local walls = {
pStaticSeg(a1, a2, a1, a3, radius, elasticity, friction, color),
pStaticSeg(a1, a3, a4, a3, radius, elasticity, friction, color),
pStaticSeg(a4, a3, a4, a2, radius, elasticity, friction, color),
pStaticSeg(a4, a2, a1, a2, radius, elasticity, friction, color)
}
for _, v in ipairs(walls) do space:addStatic(v) end
end
function polyLine(xyList, radius, elasticity, friction, color)
local lines = {}
for i = 1, #xyList - 2, 2 do
lines[i] = pStaticSeg(xyList[i], xyList[i+1], xyList[i+2], xyList[i+3], radius, elasticity, friction, color)
space:addStatic(lines[i])
end
end
function reset()
on.resize()
timeElapsed = 0
space = pSpace(GRAVITY)
fence(0, 0, W, H, 100, 1, 0)
polyLine({-12, -3, -8, -8, 8, -8, 12, -3}, 0.5, 1, 0, color.gray)
end
function on.charIn(char)
if char == "1" then
poly = pCompPoly(10, var.recall("a"), var.recall("b"), 1, 0, COLOR[math.random(#COLOR)])
space:addCompPoly(poly, 0, 0, 0, 10)
elseif char == "2" then
ball = pBall(5, 1.52, 1, 0, COLOR[math.random(#COLOR)])
space:addObj(ball, 0, 0, 0, 10)
elseif char == "3" then
reg = pRegPoly(5, 0.3, math.random(3,6), 1, 0, COLOR[math.random(#COLOR)])
space:addObj(reg, 0, 0, 0, 10)
elseif char == "4" then
poly = pIrregPoly(5, {math.random(-18,0)/10,0,0.6,1.2,1.4,-0.4,0.2,math.random(-28,-10)/10}, 1, 0, COLOR[math.random(#COLOR)])
space:addObj(poly, 0, 0, 0, 10)
elseif char == "5" then
box = pBox(4, 0.2, 3, 1, 0, COLOR[math.random(#COLOR)])
space:addObj(box, 0, 0, 0, 10)
elseif char == "6" then
poly = pCompPoly(10, var.recall("c"), var.recall("d"), 1, 0, COLOR[math.random(#COLOR)])
space:addCompPoly(poly, 0, 0, 0, 10)
end
platform.window:invalidate()
end
function on.construction() reset() end
function on.escapeKey() reset() end
function on.paint(gc)
if GRID then grid(gc) end
space:paint(gc)
end
function on.timer()
space:step(dtChipmunk)
timeElapsed = timeElapsed + dtChipmunk
platform.window:invalidate()
end
function on.enterKey()
if TICKING == false then timer.start(dtLua) TICKING = true
elseif TICKING == true then timer.stop() TICKING = false
end
end
a:=[[−2.7,0.448502757,−2.5,0.84920787,−2.5,−0.84920787,−2.7,−0.448502757][−2.5,0.84920787,−2.3,1.095971416,−2.3,−1.095971416,−2.5,−0.84920787][−2.3,1.095971416,−2.1,1.281074837,−2.1,−1.281074837,−2.3,−1.095971416][−2.1,1.281074837,−1.9,1.428688975,−1.9,−1.428688975,−2.1,−1.281074837][−1.9,1.428688975,−1.7,1.549565001,−1.7,−1.549565001,−1.9,−1.428688975][−1.7,1.549565001,−1.5,1.649591237,−1.5,−1.649591237,−1.7,−1.549565001][−1.5,1.649591237,−1.3,1.732383002,−1.3,−1.732383002,−1.5,−1.649591237][−1.3,1.732383002,−1.1,1.800319564,−1.1,−1.800319564,−1.3,−1.732383002][−1.1,1.800319564,−0.9,1.855033762,−0.9,−1.855033762,−1.1,−1.800319564][−0.9,1.855033762,−0.7,1.897669633,−0.7,−1.897669633,−0.9,−1.855033762][−0.7,1.897669633,−0.5,1.92902822,−0.5,−1.92902822,−0.7,−1.897669633][−0.5,1.92902822,−0.3,1.949653754,−0.3,−1.949653754,−0.5,−1.92902822][−0.3,1.949653754,−0.1,1.959885126,−0.1,−1.959885126,−0.3,−1.949653754][−0.1,1.959885126,0.1,1.959885126,0.1,−1.959885126,−0.1,−1.959885126][0.1,1.959885126,0.3,1.949653754,0.3,−1.949653754,0.1,−1.959885126][0.3,1.949653754,0.5,1.92902822,0.5,−1.92902822,0.3,−1.949653754][0.5,1.92902822,0.7,1.897669633,0.7,−1.897669633,0.5,−1.92902822][0.7,1.897669633,0.9,1.855033762,0.9,−1.855033762,0.7,−1.897669633][0.9,1.855033762,1.1,1.800319564,1.1,−1.800319564,0.9,−1.855033762][1.1,1.800319564,1.3,1.732383002,1.3,−1.732383002,1.1,−1.800319564][1.3,1.732383002,1.5,1.649591237,1.5,−1.649591237,1.3,−1.732383002][1.5,1.649591237,1.7,1.549565001,1.7,−1.549565001,1.5,−1.649591237][1.7,1.549565001,1.9,1.428688975,1.9,−1.428688975,1.7,−1.549565001][1.9,1.428688975,2.1,1.281074837,2.1,−1.281074837,1.9,−1.428688975][2.1,1.281074837,2.3,1.095971416,2.3,−1.095971416,2.1,−1.281074837][2.3,1.095971416,2.5,0.84920787,2.5,−0.84920787,2.3,−1.095971416][2.5,0.84920787,2.7,0.448502757,2.7,−0.448502757,2.5,−0.84920787]]
b:={0.448502757,0.84920787,1.095971416,1.281074837,1.428688975,1.549565001,1.649591237,1.732383002,1.800319564,1.855033762,1.897669633,1.92902822,1.949653754,1.959885126,1.959885126,1.949653754,1.92902822,1.897669633,1.855033762,1.800319564,1.732383002,1.649591237,1.549565001,1.428688975,1.281074837,1.095971416,0.84920787,0.448502757,−0.448502757,−0.84920787,−1.095971416,−1.281074837,−1.428688975,−1.549565001,−1.649591237,−1.732383002,−1.800319564,−1.855033762,−1.897669633,−1.92902822,−1.949653754,−1.959885126,−1.959885126,−1.949653754,−1.92902822,−1.897669633,−1.855033762,−1.800319564,−1.732383002,−1.649591237,−1.549565001,−1.428688975,−1.281074837,−1.095971416,−0.84920787,−0.448502757}
c:=[[1.41,1.41,2.12,2.12,3,0,2,0][2,0,3,0,2.12,−2.12,1.41,−1.41][1.41,−1.41,2.12,−2.12,0,−3,0,−2][0,−2,0,−3,−2.12,−2.12,−1.41,−1.41][−1.41,−1.41,−2.12,−2.12,−3,0,−2,0][−2,0,−3,0,−2.12,2.12,−1.41,1.41]]
d:={2.12,2.12,3,0,2.12,−2.12,0,−3,−2.12,−2.12,−3,0,−2.12,2.12,−1.41,1.41,−2,0,−1.41,−1.41,0,−2,1.41,−1.41,2,0,1.41,1.41}
