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apps: Improve anageo
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@johannes-wolf
johannes-wolf committed Apr 20, 2024
1 parent 80cda6c commit ceff48f
Showing 1 changed file with 208 additions and 64 deletions.
272 changes: 208 additions & 64 deletions apps/find_plane.lua
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Original file line number Diff line number Diff line change
Expand Up @@ -7,6 +7,7 @@ local choice = require('dialog.choice').display_sync
local matrix_ed = require('rpn.matrixeditor').display_sync
local expr = require 'expressiontree'
local sym = require 'ti.sym'
local fn = require 'fn'

local function table_to_vec(t)
local r = ""
Expand Down Expand Up @@ -67,94 +68,237 @@ local function ask_n_vectors(ctrl, names)
end
end

-- Find plane equation from 3 pts
local function run_plane_3pt(ctrl, stack)
local a, b, c = table.unpack(ask_n_vectors(ctrl, {"a", "b", "c"}))
local ab = math.evalStr(table_to_vec(a) .. "-" .. table_to_vec(b))
local ac = math.evalStr(table_to_vec(a) .. "-" .. table_to_vec(c))
local n = math.evalStr("crossp(" .. ab .. "," .. ac .. ")")
local eq = math.evalStr("dotp(" ..n .. "," .. table_to_vec({"x", "y", "z"}) .. ")")
local d = math.evalStr(string.format(eq .."|(x=%s and y=%s and z=%s)", a[1], a[2], a[3]))

local res_c = eq .. " = " .. d
local res_p = "x = " .. table_to_vec(a) .. " + s*" .. ab .. " + t*" .. ac
local res_n = "(x - " .. table_to_vec(a) .. ") " .. sym.CDOT .. " " .. n

local action = choice { title = 'Results', items = {
{ title = 'E: ' .. res_c, align = -1, result = 'c' },
{ title = 'E: ' .. res_p, align = -1, result = 'p' },
{ title = 'E: ' .. res_n, align = -1, result = 'n' },
{ title = 'Store...', result = 'store' },
{ title = 'Exit', result = 'done' },
}}

if action == 'store' then
local sym = ask { title = 'Variable', text = 'E1' }
if sym and #sym > 0 then
stack:push_infix(res_c)
stack:push_infix(sym)
stack:push_operator('=:')
-- Find line-point distance
local function run_line_point(ctrl)
local a, n, p = table.unpack(fn.imap(ask_n_vectors(ctrl, {"a", "n", "p"}), table_to_vec))
if a and p then
local n = math.evalStr("(" .. n .. "/norm(" .. n .. "))")
local eq = a .. "+t*".. n
local isection = "solve(" .. eq .. "=" .. p .. ",t)"
local rvec = string.format("(%s-%s)-dotp(%s-%s,%s)*%s", p, a, p, a, n, n)
local distance = "norm(" .. rvec .. ")"
local proj = string.format("%s+dotp(%s-%s,%s)*%s", a, p, a, n, n)

-- Results
local r_isection = math.evalStr(isection)
if r_isection == "false" then
r_isection = nil
end
local r_distance = math.evalStr(distance)
local r_rvec = math.evalStr(rvec)
local r_proj = math.evalStr(proj)

-- Collect results
local r = {}
if r_isection then
table.insert(r, { title = 'Point on line', result = '*' })
table.insert(r, { title = 't: ' .. r_isection, result = r_isection, align = -1 })
else
table.insert(r, { title = 'Point not on line', result = '*' })
table.insert(r, { title = 'Shortest distance: ' .. r_distance, result = r_distance, align = -1 })
table.insert(r, { title = 'Vector p to x: ' .. r_rvec, result = r_rvec, align = -1})
table.insert(r, { title = 'Projection on x: ' .. r_proj, result = r_proj, align = -1 })
end

-- Show results
table.insert(r, { title = 'Done', result = 'done' })
while true do
local action = choice {
title = 'Results',
items = r,
}
if action == 'done' then
break
elseif action then
ctrl:push_infix(tostring(action))
end
end
elseif action == 'c' then
stack:push_infix(res_c)
elseif action == 'done' then
return
end
end

-- Find intersection point or distance between two lines
local function run_2lines(ctrl, stack)
local function vec_str(l)
return string.format("[[%s,%s,%s]]", table.unpack(l))
end

local p1, d1, p2, d2 = table.unpack(ask_n_vectors(ctrl, {"p1", "d1", "p2", "d2"}))
if p1 then
local vp1, vd1 = vec_str(p1), vec_str(d1)
local vp2, vd2 = vec_str(p2), vec_str(d2)

local eq1 = vp1 .. "+a*".. vd1
local eq2 = vp2 .. "+b*".. vd2

local function run_line_line(ctrl)
local p1, d1, p2, d2 = table.unpack(fn.imap(ask_n_vectors(ctrl, {"p1", "d1", "p2", "d2"}), table_to_vec))
if p1 and p2 then
local eq1 = p1 .. "+a*".. d1
local eq2 = p2 .. "+b*".. d2
local isection = "solve(" .. eq1 .. "=" .. eq2 .. ",a,b)"
local parallel = "solve(" .. vd1 .. "=t*" .. vd2 .. ",t)"
local n = math.evalStr("crossp(" .. vd1 .. "," .. vd2 .. ")")
local n1 = math.evalStr("crossp(" .. vd1 .. "," .. n .. ")")
local n2 = math.evalStr("crossp(" .. vd2 .. "," .. n .. ")")
local parallel = "solve(" .. d1 .. "=t*" .. d2 .. ",t)"
local n = "crossp(" .. d1 .. "," .. d2 .. ")"
local n1 = "crossp(" .. d1 .. "," .. n .. ")"
local n2 = "crossp(" .. d2 .. "," .. n .. ")"
local nearest1 = string.format("%s+(dotp(%s-%s,%s)/dotp(%s,%s))*%s",
vp1, vp2, vp1, n2, vd1, n2, vd1)
p1, p2, p1, n2, d1, n2, d1)
local nearest2 = string.format("%s+(dotp(%s-%s,%s)/dotp(%s,%s))*%s",
vp2, vp1, vp2, n1, vd2, n1, vd2)
p2, p1, p2, n1, d2, n1, d2)
local distance = "norm(" .. nearest1 .. "-" .. nearest2 ..")"
local angle = "arccos(dotp(" .. d1 .. "," .. d2 .. ")/(norm(" .. d1 .. ")*norm(" .. d2 .. ")))"

-- Results
local r = {}
local r_isection = math.evalStr(isection)
if r_isection == 'false' then
r_isection = nil
end
local r_parallel = math.evalStr(parallel)
print(r_isection)
print(r_parallel)
if r_parallel == 'false' then
r_parallel = nil
end

if r_isection ~= 'false' then
return
local r_c1 = math.evalStr(nearest1)
local r_c2 = math.evalStr(nearest2)
local r_dist = math.evalStr(distance)

-- Collect results
if r_isection then
local r_angle = math.evalStr(angle)

table.insert(r, { title = 'Intersecting lines', result = '*' })
table.insert(r, { title = 'Intersection: ' .. r_c1, result = r_c1, align = -1 })
table.insert(r, { title = 'Angle: ' .. r_angle, result = r_angle, align = -1 })
elseif r_parallel then
table.insert(r, { title = 'Parallel lines', result = '*' })
table.insert(r, { title = 'Distance: ' .. r_dist, result = r_dist, align = -1 })
else
return
table.insert(r, { title = 'Skew lines', result = '*' })
table.insert(r, { title = 'Distance: ' .. r_dist, result = r_dist, align = -1 })
table.insert(r, { title = 'Nearest point on a: ' .. r_c1, result = r_c1, align = -1 })
table.insert(r, { title = 'Nearest point on b: ' .. r_c2, result = r_c2, align = -1 })
end

-- Show results
table.insert(r, { title = 'Done', result = 'done' })
while true do
local action = choice {
title = 'Results',
items = r,
}
if action == 'done' then
break
elseif action then
ctrl:push_infix(tostring(action))
end
end
end
end

local function run_angle_2vec(stack)
local a = table_to_vec(ask_vector("Vector a"))
local b = table_to_vec(ask_vector("Vector b"))
-- Find intersection point between line and plane
local function run_line_plane(ctrl)
local p0, n, l0, l = table.unpack(fn.imap(ask_n_vectors(ctrl, {"p0", "n", "l0", "ln"}), table_to_vec))
if p0 and l0 then
local parallel = "dotp(" .. n .. "," .. l .. ")=0"
local angle = "arccos(dotp(" .. n .. "," .. l .. ")/(norm(" .. n .. ")*norm(" .. l .. ")))"
local d = string.format("dotp((%s-%s),%s)/dotp(%s,%s)", p0, l0, n, l, n)
local dist = string.format("dotp((%s-%s),%s)/dotp(%s,%s)", p0, l0, n, n, n)

-- Results
local r = {}
local r_parallel = math.evalStr(parallel) == 'true'

-- Collect results
if not r_parallel then
local r_d = math.evalStr(d)
local r_angle = math.evalStr(angle)
local r_pt = math.evalStr(l0 .. "+" .. l .. "*" .. d)

table.insert(r, { title = 'Intersecting lines', result = '*' })
table.insert(r, { title = 'Intersection: ' .. r_pt, result = r_pt, align = -1 })
table.insert(r, { title = 'Angle: ' .. r_angle, result = r_angle, align = -1 })
else
local r_dist = math.evalStr(dist)
local r_in_plane = math.evalStr("dotp(" .. p0 .. "-" .. l0 .. "," .. n .. ")=0") == 'true'

if r_in_plane then
table.insert(r, { title = 'Parallel (in plane)', result = '*' })
table.insert(r, { title = 'Reason: (p0 - l0) * n = 0', result = '*', align = -1 })
else
table.insert(r, { title = 'Parallel', result = '*' })
table.insert(r, { title = 'Distance: ' .. r_dist, result = r_dist, align = -1 })
end
end

stack:push_infix("arccos(dotp(" .. a .. "," .. b .. ")/(norm(" .. a .. "*norm(" .. b .. "))")
-- Show results
table.insert(r, { title = 'Done', result = 'done' })
while true do
local action = choice {
title = 'Results',
items = r,
}
if action == 'done' then
break
elseif action then
ctrl:push_infix(tostring(action))
end
end
end
end

local function run_dist_2pt(stack)
local a = table_to_vec(ask_vector("Point A"))
local b = table_to_vec(ask_vector("Point B"))
local function run_angle_2vec(ctrl, stack)
local a, b = table.unpack(fn.imap(ask_n_vectors(ctrl, {"a", "b"}), table_to_vec))
stack:push_infix("arccos(dotp(" .. a .. "," .. b .. ")/(norm(" .. a .. ")*norm(" .. b .. "))")
end

local function run_dist_2pt(ctrl, stack)
local a, b = table.unpack(fn.imap(ask_n_vectors(ctrl, {"a", "b"}), table_to_vec))
stack:push_infix("norm(" .. b .. "-" .. a .. ")")
end

apps.add('plane - 3pt', 'Plane - 3 Points', run_plane_3pt)
local function run_convert_plane(ctrl)
local from
while not from do
from = choice {
title = 'Input format',
items = {
{ title = 'Points (a,b,c)', result = 'points' },
{ title = 'Vector ((x-p)*n=0)', result = 'vector' },
--{ title = 'Equation (x+y+z=d)', result = 'equation' },
{ title = 'Cancel', result = 'done' }
}
}
if from == 'done' then return end
end

local p0, n

if from == "points" then
local a, b, c = table.unpack(ask_n_vectors(ctrl, { "a", "b", "c" }))
if a and b and c then
local ab = table_to_vec(b) .. "-" .. table_to_vec(a)
local ac = table_to_vec(c) .. "-" .. table_to_vec(a)

p0 = table_to_vec(a)
n = "crossp(" .. ab .. "," .. ac .. ")"
end
elseif from == "vector" then
p0, n = table.unpack(fn.imap(ask_n_vectors(ctrl, { "p0", "n" }), table_to_vec))
end

local r_eq = math.evalStr("dotp([[x][y][z]]," .. n .. ")") .. "=" .. math.evalStr("dotp(" .. p0 .. "," .. n .. ")")
local r_vector = string.format("dotp((x-%s), %s)", p0, n)
local r_vector_norm = string.format("dotp((x-%s), %s)", p0, math.evalStr(n .. "/norm(" .. n .. ")"))

while true do
local action = choice {
title = "Resutl",
items = {
{ title = r_eq, result = r_eq },
{ title = r_vector, result = r_vector },
{ title = r_vector_norm, result = r_vector_norm },
{ title = 'Done', result = 'done' },
}
}
if action == 'done' then
break
elseif action then
ctrl:push_infix(action)
end
end
end

apps.add('angle - 2vec', 'Angle - 2 Vectors', run_angle_2vec)
apps.add('dist - 2pt', 'Dist. - 2 Points', run_dist_2pt)
apps.add('2line', '2line', run_2lines)

apps.add('AnaGeo: line-point', 'line-point', run_line_point)
apps.add('AnaGeo: line-line', 'line-line', run_line_line)
apps.add('AnaGeo: line-plane', 'line-plane', run_line_plane)
apps.add('AnaGeo: convert plane', 'convert plane', run_convert_plane)

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