{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1c2bb917",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "# Plot 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "845dcf1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Copyright (c) 2018-2025 William Emerison Six\n",
    "#\n",
    "# This program is free software; you can redistribute it and/or\n",
    "# modify it under the terms of the GNU General Public License\n",
    "# as published by the Free Software Foundation; either version 2\n",
    "# of the License, or (at your option) any later version.\n",
    "#\n",
    "# This program is distributed in the hope that it will be useful,\n",
    "# but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
    "# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
    "# GNU General Public License for more details.\n",
    "#\n",
    "# You should have received a copy of the GNU General Public License\n",
    "# along with this program; if not, write to the Free Software\n",
    "# Foundation, Inc., 59 Temple Place - Suite 330,\n",
    "# Boston, MA 02111-1307, USA."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b70a86ce",
   "metadata": {},
   "source": [
    "Problem 1\n",
    "---------\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "64fe7159",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "import sympy\n",
    "\n",
    "from modelviewprojection.mathutils import (\n",
    "    Vector1D,\n",
    "    Vector2D,\n",
    "    Vector3D,\n",
    "    compose,\n",
    "    compose_intermediate_fns,\n",
    "    identity,\n",
    "    inverse,\n",
    ")\n",
    "from modelviewprojection.mathutils import rotate as R\n",
    "from modelviewprojection.mathutils import scale_non_uniform_2d as S\n",
    "from modelviewprojection.mathutils import translate as T\n",
    "from modelviewprojection.nbplotutils import (\n",
    "    create_basis,\n",
    "    create_graphs,\n",
    "    create_unit_circle,\n",
    "    create_x_and_y,\n",
    "    draw_isoceles_triangle,\n",
    "    draw_right_triangle,\n",
    "    draw_screen,\n",
    "    draw_second_right_triangle,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b58e1763",
   "metadata": {},
   "outputs": [],
   "source": [
    "T(Vector1D(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "20b50649",
   "metadata": {},
   "outputs": [],
   "source": [
    "S(5, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b539e31",
   "metadata": {},
   "outputs": [],
   "source": [
    "inverse(T(Vector1D(5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5b64929e",
   "metadata": {},
   "outputs": [],
   "source": [
    "T(Vector2D(5, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8b1ea187",
   "metadata": {},
   "outputs": [],
   "source": [
    "T(Vector3D(5, 6, 7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af0f697f",
   "metadata": {},
   "outputs": [],
   "source": [
    "inverse(T(Vector3D(5, 6, 7)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2d3a0e7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "R(sympy.pi / 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6e85ad8",
   "metadata": {},
   "outputs": [],
   "source": [
    "compose([R(sympy.pi / 2), T(Vector2D(5, 6))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aab6550a",
   "metadata": {},
   "outputs": [],
   "source": [
    "inverse(compose([R(sympy.pi / 2), T(Vector2D(5, 6))]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "520df956",
   "metadata": {},
   "source": [
    "Draw graph paper\n",
    "----------------\n",
    "\n",
    "Just draw graph paper, where one unit in the x direction is blue,\n",
    "and one unit in the y direction is pink.  The graph paper corresponds\n",
    "to the numbers on the left and on the bottom.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3187d56f",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "fn = R(math.radians(53.130102))\n",
    "with create_graphs(graph_bounds=(5, 5)) as axes:\n",
    "    create_basis(fn=fn)\n",
    "    create_x_and_y(fn=fn)\n",
    "    create_unit_circle(fn=fn)\n",
    "    axes.set_title(fn._repr_latex_())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25098879",
   "metadata": {},
   "source": [
    "Draw relative graph paper\n",
    "-------------------------\n",
    "\n",
    "Draw two relative number lines, making a relative graph paper,\n",
    "but keep the original coordinate system on the left and bottom.\n",
    "Any point in the plane can be described using two different\n",
    "graph papers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4dd64f1d",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "fn = R(math.radians(53.130102))\n",
    "with create_graphs(graph_bounds=(5, 5)) as axes:\n",
    "    create_basis(fn=R(0.0))\n",
    "    create_x_and_y(fn=R(0.0))\n",
    "    create_basis(\n",
    "        fn=fn,\n",
    "        xcolor=(0, 1, 0),\n",
    "        ycolor=(1, 1, 0),\n",
    "    )\n",
    "    create_x_and_y(\n",
    "        fn=fn,\n",
    "        xcolor=(0, 1, 0),\n",
    "        ycolor=(1, 1, 0),\n",
    "    )\n",
    "    create_unit_circle(fn=fn)\n",
    "    axes.set_title(fn._repr_latex_())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6539400e",
   "metadata": {},
   "source": [
    "Draw relative graph paper\n",
    "-------------------------\n",
    "\n",
    "Draw two relative number lines, making a relative graph paper,\n",
    "but keep the original coordinate system on the left and bottom.\n",
    "Any point in the plane can be described using two different\n",
    "graph papers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8efe6aec",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "fn = R(math.radians(53.130102))\n",
    "with create_graphs(graph_bounds=(5, 5)) as axes:\n",
    "    create_basis(fn=R(0.0))\n",
    "    create_x_and_y(fn=R(0.0))\n",
    "    create_basis(\n",
    "        fn=fn,\n",
    "        xcolor=(0, 1, 0),\n",
    "        ycolor=(1, 1, 0),\n",
    "    )\n",
    "    create_x_and_y(\n",
    "        fn=fn,\n",
    "        xcolor=(0, 1, 0),\n",
    "        ycolor=(1, 1, 0),\n",
    "    )\n",
    "    create_unit_circle(fn=fn)\n",
    "    draw_right_triangle()\n",
    "    draw_second_right_triangle()\n",
    "    axes.set_title(fn._repr_latex_())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d4561a0",
   "metadata": {},
   "source": [
    "Draw relative graph paper, defined by composed functions\n",
    "--------------------------------------------------------\n",
    "\n",
    "Draw a translated and rotated graph paper.\n",
    "You can read the sequence of composed functions\n",
    "in the order that they are applied, or in reverse order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c53099eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "fn = compose(\n",
    "    [\n",
    "        R(sympy.pi / 4),\n",
    "        T(Vector2D(x=2.0, y=0.0)),\n",
    "    ]\n",
    ")\n",
    "with create_graphs() as axes:\n",
    "    create_basis(\n",
    "        fn=fn,\n",
    "    )\n",
    "    create_x_and_y(fn=fn)\n",
    "    create_unit_circle(fn=fn)\n",
    "    axes.set_title(fn._repr_latex_())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e0f09d4",
   "metadata": {},
   "source": [
    "Composed functions, read bottom up\n",
    "----------------------------------\n",
    "\n",
    "The sequence of functions shown, where the translate\n",
    "is applied first, and operations are relative to the\n",
    "units on the left and bottom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f118c9a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "for f in compose_intermediate_fns([R(sympy.pi / 4), T(Vector2D(x=2.0, y=0.0))]):\n",
    "    # TODO - figure out if I can render the latex as part of one markdown command,\n",
    "    # if I were to uncomment out this line and other markdown lines,\n",
    "    # the build of HTML would fail\n",
    "\n",
    "    with create_graphs() as axes:\n",
    "        create_basis(fn=f)\n",
    "        create_x_and_y(fn=f)\n",
    "        create_x_and_y()\n",
    "        draw_isoceles_triangle(fn=f)\n",
    "        create_unit_circle(fn=f)\n",
    "        create_unit_circle()\n",
    "        axes.set_title(f._repr_latex_())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c39eee95",
   "metadata": {},
   "source": [
    "Composed functions, read top down\n",
    "---------------------------------\n",
    "\n",
    "The sequence of functions shown, where we visualize\n",
    "the rotate first, and then the translate relative to\n",
    "that relative graph paper.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07523f4a",
   "metadata": {
    "lines_to_next_cell": 0
   },
   "outputs": [],
   "source": [
    "for f in compose_intermediate_fns(\n",
    "    [\n",
    "        R(sympy.pi / 4),\n",
    "        T(Vector2D(x=1.0, y=0.0)),\n",
    "    ],\n",
    "    relative_basis=True,\n",
    "):\n",
    "    with create_graphs() as axes:\n",
    "        create_basis(fn=f)\n",
    "        create_x_and_y(fn=f)\n",
    "        draw_isoceles_triangle(fn=f)\n",
    "        create_unit_circle(fn=f)\n",
    "        axes.set_title(f._repr_latex_())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "721d6804",
   "metadata": {
    "lines_to_next_cell": 0
   },
   "outputs": [],
   "source": [
    "screen_width: int = 4\n",
    "screen_height: int = 3\n",
    "\n",
    "for f in compose_intermediate_fns(\n",
    "    [\n",
    "        T(Vector2D(-0.5, -0.5)),\n",
    "        S(screen_width, screen_height),\n",
    "        S(0.5, 0.5),\n",
    "        T(Vector2D(x=1.0, y=1.0)),\n",
    "    ],\n",
    "    relative_basis=False,\n",
    "):\n",
    "    with create_graphs(graph_bounds=(6, 6)) as axes:\n",
    "        # create_basis(fn=f)\n",
    "        # create_x_and_y(fn=f)\n",
    "        create_basis(fn=identity())\n",
    "        create_x_and_y(fn=identity())\n",
    "        # draw_ndc(fn=f)\n",
    "        draw_screen(width=screen_width, height=screen_height, fn=f)\n",
    "        axes.set_title(f._repr_latex_())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "86508fd2",
   "metadata": {},
   "outputs": [],
   "source": [
    "screen_width: int = 4\n",
    "screen_height: int = 3\n",
    "\n",
    "for f in compose_intermediate_fns(\n",
    "    [\n",
    "        T(Vector2D(-0.5, -0.5)),\n",
    "        S(screen_width, screen_height),\n",
    "        S(0.5, 0.5),\n",
    "        T(Vector2D(x=1.0, y=1.0)),\n",
    "    ],\n",
    "    relative_basis=True,\n",
    "):\n",
    "    with create_graphs(graph_bounds=(6, 6)) as axes:\n",
    "        # create_basis(fn=f)\n",
    "        # create_x_and_y(fn=f)\n",
    "        create_basis(fn=identity())\n",
    "        create_x_and_y(fn=f)\n",
    "        # draw_ndc(fn=f)\n",
    "        draw_screen(width=screen_width, height=screen_height, fn=f)\n",
    "        axes.set_title(f._repr_latex_())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d30b1619",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f47fc2f5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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