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-- This file:
-- http://angg.twu.net/LUA/Pict3D1.lua.html
-- http://angg.twu.net/LUA/Pict3D1.lua
-- (find-angg "LUA/Pict3D1.lua")
-- Author: Eduardo Ochs <eduardoochs@gmail.com>
--
-- Support for 3D, version for Pict2e1.lua.
-- See: (find-angg "LUA/Pict2e1.lua")
-- (find-angg "LUA/Pict2e1-1.lua")
-- (find-angg "LUA/Piecewise1.lua")
-- (c3m212nfp 32 "quadraticas-exemplos")
-- (c3m212nfa "quadraticas-exemplos")
-- (find-LATEX "2021-1-C3-3D.lua")
--
-- (defun a () (interactive) (find-angg "LUA/Pict2e1.lua"))
-- (defun b () (interactive) (find-angg "LUA/Pict3D1.lua"))
-- (defun ab () (interactive) (find-2b '(a) '(b)))
-- (defun et () (interactive) (find-angg "LATEX/2022pict2e.tex"))
-- (defun eb () (interactive) (find-angg "LATEX/2022pict2e-body.tex"))
-- (defun ao () (interactive) (find-angg "LATEX/2022pict2e.lua"))
-- (defun v () (interactive) (find-pdftools-page "~/LATEX/2022pict2e.pdf"))
-- (defun tb () (interactive) (find-ebuffer (eepitch-target-buffer)))
-- (defun etv () (interactive) (find-wset "13o2_o_o" '(tb) '(v)))
-- (setenv "PICT2ELUADIR" "~/LATEX/")
--
-- (find-LATEXgrep "grep --color=auto -niH --null -e piecewise *.tex *.lua")
-- «.V3» (to "V3")
-- «.V3-tests» (to "V3-tests")
-- «.Line3D» (to "Line3D")
-- «.Line3D-tests» (to "Line3D-tests")
-- «.Pict2Dify» (to "Pict2Dify")
-- «.Pict2Dify-tests» (to "Pict2Dify-tests")
-- «.pictreplace» (to "pictreplace")
-- «.Surface» (to "Surface")
-- «.Surface-tests» (to "Surface-tests")
-- «.QuadraticFunction» (to "QuadraticFunction")
-- «.QuadraticFunction-tests» (to "QuadraticFunction-tests")
-- «.nff» (to "nff")
-- «.nff-test1» (to "nff-test1")
-- «.nff-test2» (to "nff-test2")
-- «.ThreeD» (to "ThreeD")
-- «.ThreeD-tests» (to "ThreeD-tests")
require "Pict2e1" -- (find-angg "LUA/Pict2e1.lua")
require "Pict2e1-1" -- (find-angg "LUA/Pict2e1-1.lua")
tow = function (vv, ww, a, b)
local diff = ww-vv
-- local diffrot90 = v(diff[2], -diff[1])
return vv + (a or 0.5)*diff -- + (b or 0)*diffrot90
end
-- «V3» (to ".V3")
-- (find-es "dednat" "V3")
--
V3 = Class {
type = "V3",
__tostring = function (v) return v:tostring() end,
__add = function (v, w) return V3{v[1]+w[1], v[2]+w[2], v[3]+w[3]} end,
__sub = function (v, w) return V3{v[1]-w[1], v[2]-w[2], v[3]-w[3]} end,
__unm = function (v) return v*-1 end,
__mul = function (v, w)
local ktimesv = function (k, v) return V3{k*v[1], k*v[2], k*v[3]} end
local innerprod = function (v, w) return v[1]*w[1] + v[2]*w[2] + v[3]*w[3] end
if type(v) == "number" and type(w) == "table" then return ktimesv(v, w)
elseif type(v) == "table" and type(w) == "number" then return ktimesv(w, v)
elseif type(v) == "table" and type(w) == "table" then return innerprod(v, w)
else error("Can't multiply "..tostring(v).."*"..tostring(w))
end
end,
__index = {
tostring = function (v) return v:v3string() end,
v3string = function (v) return pformat("(%s,%s,%s)", v[1], v[2], v[3]) end,
v2string = function (v) return tostring(v:tov2()) end,
--
-- Convert v3 to v2 using a primitive kind of perspective.
-- Adjust p1, p2, p3 to change the perspective.
tov2 = function (v) return v[1]*v.p1 + v[2]*v.p2 + v[3]*v.p3 end,
p1 = V{2,-1},
p2 = V{2,1},
p3 = V{0,2},
--
Line = function (A, v) return Line3D.from(A, A+v) end,
Lines = function (A, v, w, i, j)
local p = PictList {}
for k=i,j do table.insert(p, (A+k*w):Line(v)) end
return p
end,
--
xticks = function (_,n,eps)
eps = eps or 0.15
return v3(0,-eps,0):Lines(v3(0,2*eps,0), v3(1,0,0), 0, n)
end,
yticks = function (_,n,eps)
eps = eps or 0.15
return v3(-eps,0,0):Lines(v3(2*eps,0,0), v3(0,1,0), 0, n)
end,
zticks = function (_,n,eps)
eps = eps or 0.15
return v3(-eps,0,0):Lines(v3(2*eps,0,0), v3(0,0,1), 0, n)
end,
axeswithticks = function (_,x,y,z)
local p = PictList {}
table.insert(p, v3(0,0,0):Line(v3(x+0.5, 0, 0)))
table.insert(p, v3(0,0,0):Line(v3(0, y+0.5, 0)))
table.insert(p, v3(0,0,0):Line(v3(0, 0, z+0.5)))
table.insert(p, _:xticks(x))
table.insert(p, _:yticks(y))
table.insert(p, _:zticks(z))
return p
end,
xygrid = function (_,x,y)
return PictList {
v3(0,0,0):Lines(v3(0,y,0), v3(1,0,0), 0, x),
v3(0,0,0):Lines(v3(x,0,0), v3(0,1,0), 0, y)
}
end,
gat = function (_,x,y,z)
return PictList {
_:xygrid (x, y ):Color("Gray"),
_:axeswithticks(x, y, z)
}
end,
},
}
v3 = function (x,y,z) return V3{x,y,z} end
-- Choose one:
V3.__index.tostring = function (v) return v:v2string() end
V3.__index.tostring = function (v) return v:v3string() end
-- (find-LATEX "2022pict2e.lua" "Surface")
-- «V3-tests» (to ".V3-tests")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Pict3D1.lua"
vv = v3(1, 2, 3)
ww = v3(10, 100, 1000)
= vv
= vv + ww
= - (vv + 10*ww)
= vv:xticks(2)
= vv:Line(ww)
= vv:xygrid(2, 3)
= vv:axeswithticks(2, 3, 4)
= vv:axeswithticks(2, 3, 4):twod()
= vv:gat(4, 3, 2)
= vv:gat(4, 3, 2):twod()
V3.__index.p1 = V{2, -0.5}
V3.__index.p2 = V{0.5, 1.7}
V3.__index.p3 = V{0, 0.5}
Pict2e.bounds = PictBounds.new(v(0,-2), v(9.5,6))
= vv:gat(4, 3, 2):twod()
= vv:gat(4, 3, 2):twod():bshow("Bp")
* (etv)
--]]
-- _ _ _____ ____
-- | | (_)_ __ ___|___ /| _ \
-- | | | | '_ \ / _ \ |_ \| | | |
-- | |___| | | | | __/___) | |_| |
-- |_____|_|_| |_|\___|____/|____/
--
-- «Line3D» (to ".Line3D")
-- (find-angg "LUA/Pict2e1.lua" "PictSub")
Line3D = PradClass.from {
type = "Line3D",
from = function (...)
return Line3D { ... }
end,
__tostring = function (l3)
return (l3.op or "\\Line")..mapconcat(tostring, l3)
end,
__index = {
addpoint = function (l3, p) table.insert(l3, p); return l3 end,
print = function (l3, out, ctx)
l3:printitem(out, ctx, tostring(l3))
end,
},
}
-- «Line3D-tests» (to ".Line3D-tests")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Pict3D1.lua"
l3a = Line3D.from(v3(1,2,3), v3(4,5,6))
l3b = Line3D.from(v3(1,2,3), v3(4,5,6), v3(7,8,9))
l3s = PictSub { l3a, PictSub { l3a, l3b } }
= l3s
V3.__index.tostring = function (v) return v:v2string() end
= l3s
V3.__index.tostring = function (v) return v:v3string() end
= l3s
--]]
-- ____ _ _ ____ ____ _ __
-- | _ \(_) ___| |_|___ \| _ \(_)/ _|_ _
-- | |_) | |/ __| __| __) | | | | | |_| | | |
-- | __/| | (__| |_ / __/| |_| | | _| |_| |
-- |_| |_|\___|\__|_____|____/|_|_| \__, |
-- |___/
-- «Pict2Dify» (to ".Pict2Dify")
-- (find-angg "LUA/Pict2e1.lua" "PictSub")
Pict2Dify = PradClass.from {
type = "Pict2Dify",
__tostring = function (p) return p:tostring() end,
__index = {
print = function (p, out, ctx)
local oldV3tostring = V3.__index.tostring
V3.__index.tostring = function (v) return v:v2string() end
p:printitems(out, ctx)
V3.__index.tostring = oldV3tostring
end,
},
}
PradClass.__index.twod = function (p)
return Pict2Dify { p }
end
-- «Pict2Dify-tests» (to ".Pict2Dify-tests")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Pict3D1.lua"
l3a = Line3D.from(v3(1,2,3), v3(4,5,6))
l3b = Line3D.from(v3(1,2,3), v3(4,5,6), v3(7,8,9))
l3s = PictSub { l3a, PictSub { l3a, l3b } }
= l3s
= PictList { Pict2Dify { l3a, l3s }, l3a }
= PictList { l3s:twod(), l3s }
--]]
-- «pictreplace» (to ".pictreplace")
-- (find-es "dednat" "pictreplace")
--
-- pictreplace = function (bigstr)
-- -- local f = function (code) return tostring(expr(code)) end
-- local f = function (code) return deletecomments(tostring(expr(code))) end
-- local g = function (line) return (line:gsub("<([^<>]+)>", f)) end
-- return (bigstr:gsub("[^\n]+", g))
-- end
--
-- registerhead "%P" {
-- name = "pictreplace",
-- action = function ()
-- local i,j,pictcode = tf:getblockstr(3)
-- output(pictreplace(pictcode))
-- end,
-- }
-- «Surface» (to ".Surface")
-- (find-dn6 "picture.lua" "V")
-- (find-dn6 "diagforth.lua" "newnode:at:")
--
Surface = Class {
type = "Surface",
new = function (f, x0, y0)
return Surface {f=f, x0=x0, y0=y0, xy0=v(x0, y0)}
end,
__index = {
xyz = function (s, xy, zvalue)
return v3(xy[1], xy[2], zvalue or s.f(xy[1], xy[2]))
end,
xyztow = function (s, xy1, xy2, zvalue, k)
return s:xyz(tow(xy1, xy2, k), zvalue)
end,
segment = function (s, xy1, xy2, zvalue, n)
local seg = Line3D.from()
for i=0,n do seg:addpoint(s:xyztow(xy1, xy2, zvalue, i/n)) end
return seg
end,
pillar = function (s, xy)
return Line3D.from(s:xyz(xy, 0), s:xyz(xy, nil))
end,
pillars = function (s, xy1, xy2, n)
local pils = PictList {}
for i=0,n do table.insert(pils, s:pillar(tow(xy1, xy2, i/n))) end
return pils
end,
--
segmentstuff = function (s, xy1, xy2, n, what)
local stf = PictList {}
if what:match"0" then table.insert(stf, s:segment(xy1, xy2, 0, 1)) end
if what:match"c" then table.insert(stf, s:segment(xy1, xy2, nil, n)) end
if what:match"p" then table.insert(stf, s:pillars(xy1, xy2, n)) end
return stf
end,
--
stoxy = function (s, str)
expr(format("v(%s)", str))
end,
squarestuff = function (s, dxy0s, dxy1s, n, what)
local dxy0 = expr(format("v(%s)", dxy0s))
local dxy1 = expr(format("v(%s)", dxy1s))
local xy1 = s.xy0 + dxy0
local xy2 = s.xy0+dxy1
return s:segmentstuff(xy1, xy2, n, what)
end,
squarestuffp = function (s, n, what, pair)
local dxy0,dxy1 = unpack(split(pair))
return s:squarestuff(dxy0, dxy1, n, what)
end,
squarestuffps = function (s, n, what, listofpairs)
local stf = PictList {}
for _,pair in ipairs(listofpairs) do
table.insert(stf, s:squarestuffp(n, what, pair))
end
return stf
end,
--
horizontals = function (s, n, what)
return s:squarestuffps(n, what, {
"-1,-1 1,-1", "-1,0 1,0", "-1,1 1,1"
})
end,
verticals = function (s, n, what)
return s:squarestuffps(n, what, {
"-1,-1 -1,1", "0,-1 0,1", "1,-1 1,1"
})
end,
diagonals = function (s, n, what)
return s:squarestuffps(n, what, {
"-1,-1 1,1", "-1,1 1,-1"
})
end,
square = function (s, n, what)
return PictList { s:horizontals(n, what),
s:verticals (n, what) }
end,
},
}
-- «Surface-tests» (to ".Surface-tests")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Pict3D1.lua"
F = function (x, y) return 10*x + y end
srf = Surface.new(F, 3, 4)
= srf:xyz(v(2, 5))
= srf:xyz(v(2, 5), 0)
= srf:xyztow(v(2,5), v(22,25), nil, 0.5)
= srf:xyztow(v(2,5), v(22,25), 0, 0.5)
= srf:segment(v(2,5), v(22,25), 0, 2)
= srf:segment(v(2,5), v(22,25), nil, 2)
= srf:pillar(v(2,5))
= srf:segmentstuff(v(2,5), v(22,25), 2, "0cp")
= srf:squarestuff("0,0", "2,2", 2, "0")
= srf:squarestuff("0,0", "2,2", 2, "c")
= srf:squarestuff("0,0", "2,2", 2, "p")
= srf:squarestuffp( 2, "p", "0,0 2,2")
= srf:square (2, "p")
= srf:square (4, "p")
= srf:square (2, "c")
= srf:square (4, "c")
= srf:square (8, "c")
= srf:diagonals(2, "p")
fw = function (x) return max(min(x-2, 6-x), 0) end
FP = function (x,y) return min(fw(x), fw(y)) end
FC = function (x,y) return max(fw(x), fw(y)) end
sP = Surface.new(FP, 4, 4)
= sP:segment(v(0,4), v(6,4), nil, 6)
-- ^ Used by:
-- (c3m211cnp 15 "figura-piramide")
-- (c3m211cna "figura-piramide")
-- (c3m211cnp 16 "cruz")
-- (c3m211cna "cruz")
--]]
-- «QuadraticFunction» (to ".QuadraticFunction")
--
QuadraticFunction = Class {
type = "QuadraticFunction",
__call = function (q, ...) return q:f(...) end,
__index = {
f = function (q, x, y)
local dx,dy = x - (q.x0 or 0), y - (q.y0 or 0)
return (q.a or 0)
+ (q.Dx or 0) * dx + (q.Dy or 0) * dy
+ (q.Dxx or 0) * dx*dx + (q.Dyy or 0) * dy*dy
+ (q.Dxy or 0) * dx*dy
end,
},
}
-- «QuadraticFunction-tests» (to ".QuadraticFunction-tests")
-- Used by: (c3m211qp 2 "figuras-3D")
-- (c3m211qa "figuras-3D")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "2021-1-C3-3D.lua"
qf = QuadraticFunction {x0=3, y0=2, a=100, Dx=0, Dy=0, Dxx=1, Dyy=1, Dxy=0}
= qf(3, 2)
= qf(3 + 1, 2)
= qf(3 + 1, 2 + 1)
qf = QuadraticFunction {Dx=10, Dy=1}
= qf(2, 3)
qf = QuadraticFunction {Dx=10, Dy=1, x0=20, y0=30, a=100}
= qf(20, 30)
= qf(22, 33)
qf = QuadraticFunction {Dxx=100, Dxy=10, Dyy=1}
= qf(2, 3)
= qf(2, 0)
= qf(0, 3)
--]]
-- __ __
-- _ __ / _|/ _|
-- | '_ \| |_| |_
-- | | | | _| _|
-- |_| |_|_| |_|
--
-- «nff» (to ".nff")
-- Define a function in "notação de físicos".
nff = function (str)
return Code.vc("x,y => local Dx,Dy = x-x0,y-y0; return "..str)
end
-- «nff-test1» (to ".nff-test1")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Pict3D1.lua"
x0,y0 = 3,2
= nff "Dx^2"
= nff "Dx^2"(5,5)
F = nff " Dx + Dy + 2 "
= F(3,2)
= F(4,2)
= F(4,3)
function (x, y) return 10*x + y end
srf = Surface.new(F, 3, 4)
= srf:xyz(v(2, 5))
= srf:xyz(v(2, 5), 0)
V3.__index.p1 = V{2, -0.5}
V3.__index.p2 = V{0.5, 1.7}
V3.__index.p3 = V{0, 0.5}
Pict2e.bounds = PictBounds.new(v(0,-2), v(9.5,6))
= vv:gat(4, 3, 2):twod()
= vv:gat(4, 3, 2):twod():bshow("Bp")
* (etv)
--]]
-- «nff-test2» (to ".nff-test2")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Pict3D1.lua"
V3.__index.p1 = V{2, -0.5}
V3.__index.p2 = V{0.5, 1.7}
V3.__index.p3 = V{0, 0.5}
Pict2e.bounds = PictBounds.new(v(0,-2), v(9.5,6))
bg = v3():gat(4, 3, 2)
x0,y0 = 3, 2
F = nff " Dx^2 - Dy^2 + 2 "
srf = Surface.new(F, x0, y0)
fg = PictList {
srf:square( 1, "0"),
srf:square( 1, "p"):Color("Gray"),
srf:square(16, "c")
}
p = PictList { bg, fg }
= p
= p:twod():bshow("p")
* (etv)
--]]
-- _____ _ ____
-- |_ _| |__ _ __ ___ ___| _ \
-- | | | '_ \| '__/ _ \/ _ \ | | |
-- | | | | | | | | __/ __/ |_| |
-- |_| |_| |_|_| \___|\___|____/
--
-- «ThreeD» (to ".ThreeD")
-- Some common settings for 3D diagrams.
ThreeD = Class {
type = "ThreeD",
set_432 = function ()
V3.__index.p1 = V{2, -0.5}
V3.__index.p2 = V{0.5, 1.7}
V3.__index.p3 = V{0, 0.5}
Pict2e.bounds = PictBounds.new(v(0,-2), v(9.5,6))
bg = v3():gat(4, 3, 2)
x0,y0 = 3, 2
end,
drawsurface = function (F)
srf = Surface.new(F, x0, y0)
return PictList {
bg,
srf:square( 1, "0"),
srf:square( 1, "p"):Color("Gray"),
srf:square(16, "c")
}
end,
__index = {
},
}
-- «ThreeD-tests» (to ".ThreeD-tests")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Pict3D1.lua"
ThreeD.set_432()
p = PictList {
ThreeD.drawsurface(nff " Dx^2 + Dy^2 + 2 "):pgat("p"), "\quad",
ThreeD.drawsurface(nff " Dx^2 - Dy^2 + 2 "):pgat("p")
}
p:twod():bshow("")
* (etv)
--]]
-- (defun e () (interactive) (find-angg "LUA/Pict3D1.lua"))
-- Local Variables:
-- coding: utf-8-unix
-- End: