WIP - Features, Fixes and Apps (#45)

Various fixes

.gitignore

@@ -0,0 +1,4 @@
+
+/.luna
+bundle.lua
+rpn.tns

app.lua

@@ -3,7 +3,9 @@ platform.apiLevel = '2.4'
 -- luacheck: ignore platform
 -- luacheck: ignore on
 
+local advice = require 'advice'
 local ui = require 'ui'
+local config = require 'config.config'
 require 'views.menu'
 require 'views.edit'
 require 'views.label'
@@ -17,6 +19,14 @@ require 'stringext'
 local dlg_error = require 'dialog.error'
 local rpn_controller = require 'rpn.controller'
 
+local function draw_logo(gc, frame)
+   local center = frame:center()
+   gc:set_font(nil, "b", 80)
+   gc:draw_text("rpn", 0, 0, frame.width/2, frame.height, 1, 0)
+   gc:set_font(nil, "bi", 80)
+   gc:draw_text("spire", frame.width/2, 0, frame.width/2, frame.height, -1, 0)
+ end
+
 local function build_main_view()
    local edit_height = 20
 
@@ -27,6 +37,13 @@ local function build_main_view()
    main_view:add_child(edit)
 
    local list = ui.list(ui.rel({ top = 0, bottom = edit_height, left = 0, right = 0 }))
+   if config.enable_splash then
+      list.draw_self = advice.after(list.draw_self, function(self, gc, dirty)
+         if not self.items or #self.items == 0 then
+            draw_logo(gc, self:frame())
+         end 
+      end)
+   end
    main_view:add_child(list)
 
    local controller = rpn_controller.new(main_view, edit, list)

apps/AnaGeo.lua

@@ -0,0 +1,321 @@
+local apps       = require 'apps.apps'
+local matrix     = require 'matrix'
+local advice     = require 'advice'
+local ask        = require('dialog.input').display_sync
+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'
+
+-- Eval formatted string
+local function E(fmt, ...)
+   return math.evalStr(string.format(fmt, ...))
+end
+
+-- Show results as cohice
+local function show_results(ctrl, items)
+   table.insert(items, { title = 'Done', result = 'done', align = 0 })
+
+   local action
+   while not action do
+      action = choice({title = 'Results', items = items})
+      if action == 'done' then
+         return action
+      elseif type(action) == 'function' then
+         action = action(ctrl)
+      end
+      if action and action ~= '*' then
+         ctrl:push_infix(action)
+         action = nil
+      end
+   end
+   return action
+end
+
+-- Convert lua table to nspire column vector [[x][y]...]
+local function table_to_vec(t)
+   local r = ""
+   for _, v in ipairs(t) do
+      r = r .. "[" .. v .. "]"
+   end
+   return "[" .. r .. "]"
+end
+
+-- Ask for a list of n vectors of dimension dim using the matrix editor
+local function ask_n_vectors(ctrl, names, dim)
+   local elems = {"x", "y", "z", "w"}
+   local mat = matrix.new(4, 5)
+   dim = dim or 3
+   mat:set(1,1," ")
+   for i = 1, dim do
+      mat:set(1 + i,1, elems[i])
+   end
+   mat:resize(4, 1 + #names)
+   for n = 1, #names do
+      mat:set(1, 1 + n, tostring(names[n]))
+   end
+
+   local function setup_dlg(dlg)
+      local grid = dlg.grid
+      grid:set_header(1,1)
+      grid:set_selection(2,2)
+      dlg.grid_resize(1 + dim, 1 + #names)
+   end
+
+   local res = matrix_ed(ctrl, mat, setup_dlg)
+   if res then
+      local vecs = {}
+      for n = 1, #names do
+         local v = {}
+         for i = 1, dim do
+            table.insert(v, mat:get(1 + i, n + 1))
+         end
+         table.insert(vecs, v)
+      end
+      return vecs
+   end
+end
+
+-- 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 })
+         table.insert(r, { title = "Details...", result = "" })
+      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
+      show_results(ctrl, r)
+   end
+end
+
+-- Find intersection point or distance between two lines
+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(" .. 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",
+        p1, p2, p1, n2, d1, n2, d1)
+      local nearest2 = string.format("%s+(dotp(%s-%s,%s)/dotp(%s,%s))*%s",
+        p2, p1, p2, n1, d2, n1, d2)
+      local distance = "abs(norm(" .. nearest1 .. "-" .. nearest2 .."))"
+      local angle = "arccos(abs(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)
+      if r_parallel == 'false' then
+         r_parallel = nil
+      end
+
+      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
+         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
+      show_results(ctrl, r)
+   end
+end
+
+-- 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 = "arcsin(abs(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("abs(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
+
+      -- Show results
+      show_results(ctrl, r)
+   end
+end
+
+local function run_plane_point(ctrl)
+   local p0, n, p = table.unpack(fn.imap(ask_n_vectors(ctrl, {"p0", "n", "p"}), table_to_vec))
+   if p0 and n and p then
+      local signed_dist = E("dotp((%s-%s),%s)/dotp(%s,%s)", p0, p, n, n, n)
+      local abs_dist = E("abs(%s)", signed_dist)
+      local point = E("%s+%s*%s", p, signed_dist, n)
+
+      -- Results
+      local r = {}
+
+      table.insert(r, { title = 'Distance: ' .. abs_dist, result = abs_dist })
+      table.insert(r, { title = 'Signed distance: ' .. signed_dist, result = signed_dist })
+      table.insert(r, { title = 'Point on plane: ' .. point, result = point })
+
+      -- Show results
+      show_results(ctrl, r)
+   end
+end
+
+local function run_plane_plane(ctrl)
+   local p0, n0, p1, n1 = table.unpack(fn.imap(ask_n_vectors(ctrl, {"p0", "n0", "p1", "n1"}), table_to_vec))
+   if p0 and p1 then
+      local is_parallel = E("norm(crossp(%s,%s))=0", n0, n1)
+      print(is_parallel)
+      is_parallel = is_parallel == "true"
+
+      -- Results
+      local r = {}
+
+      if not is_parallel then
+         local angle = E("arccos(abs(dotp(%s,%s))/abs(norm(%s)*norm(%s)))", n0, n1, n0, n1)
+         table.insert(r, { title = 'Angle: ' .. angle, result = angle })
+         --table.insert(r, { title = 'Intersection: ' .. intersection, result = intersection })
+      else
+         local dist = E("abs(dotp((%s-%s),%s))/dotp(%s,%s)", p0, p1, n0, n0, n0)
+         table.insert(r, { title = 'Distance: ' .. dist, result = dist })
+      end
+
+      show_results(ctrl, r)
+   end
+end
+
+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))
+   elseif from == "equation" then
+      a, b, c, d = table.unpack(fn.imap(ask_n_vectors(ctrl, { "ax", "by", "cz", "d" }, 1), function(l) return l[1] end))
+
+      p0 = {}
+      local i = 1
+      for k, v in pairs({x = a, y = b, z = c}) do
+         local is_set = math.evalStr(v .. "=0") == 'false'
+         if is_set then
+            p0[i] = d .. "/" .. v
+         else
+            p0[i] = "0"
+         end
+      end
+
+      if #p0 > 0 then
+         p0 = table_to_vec(p0)
+         n = table_to_vec({a, b, c})
+      else
+         error("Invalid plane coefficients")
+      end
+   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 .. ")"))
+
+   show_results(ctrl, {
+      { title = r_eq, result = r_eq, align = -1 },
+      { title = r_vector, result = r_vector, align = -1 },
+      { title = r_vector_norm, result = r_vector_norm, align = -1 },
+   })
+end
+
+apps.add('AnaGeo: line-point',    'l-pt', run_line_point)
+apps.add('AnaGeo: line-line',     'l-l',  run_line_line)
+apps.add('AnaGeo: line-plane',    'l-pl', run_line_plane)
+apps.add('AnaGeo: plane-point',   'pl-pt', run_plane_point)
+apps.add('AnaGeo: plane-plane',   'pl-pl', run_plane_plane)
+apps.add('AnaGeo: convert plane', 'cnv-pl', run_convert_plane)