LukashevaCurved/OrigamiSignals.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPxub7wE4qRttEKz03SrCC3",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/eleciawhite/origami/blob/main/LukashevaCurved/OrigamiSignals.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "This script explores how origami can be made of different mathematical functions and rotations. It is not intended to be used by anyone by me (Elecia White). If you do end up here, you may want to look at my [KateTess colab](https://colab.research.google.com/drive/1fzYIjLuT9UMiUwyxtAOIls0isZT1IvX4?usp=sharing) first as there is some overlap in functions and that is better documented. Or at my [YoshiSines colab](https://colab.research.google.com/drive/1OE3RBsKrw5A8SIV6d2B1cbP3igKiKiIU?usp=sharing) if that is what you are looking for."
      ],
      "metadata": {
        "id": "b-RzlivYOIZK"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "p56Kzq2A31to"
      },
      "outputs": [],
      "source": [
        "from math import *\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from matplotlib import collections  as mc\n",
        "from matplotlib.patches import Ellipse, Wedge, Polygon\n",
        "from matplotlib.path import Path\n",
        "import matplotlib\n",
        "import itertools\n",
        "\n",
        "from scipy.spatial import distance\n",
        "from scipy import signal\n",
        "import scipy\n",
        "from google.colab import files\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "I want to be able to use the Amanda Ghassaei's [Origami Simulator](https://origamisimulator.org/) to test the output of the script. \n",
        "\n",
        "In this next block, I'm fixing up the matplotlib output to be more compatible with the simulator."
      ],
      "metadata": {
        "id": "t72uLZWa4FbH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "indef = False\n",
        "def rm_clippath(line):\n",
        "  global indef\n",
        "\n",
        "  if not indef:\n",
        "    f = line.find('<clipPath')\n",
        "  else:\n",
        "    f = line.find('</clipPath>')\n",
        "  if f >= 0:\n",
        "    indef = not indef\n",
        "    return \"\"\n",
        "  if indef: return \"\"\n",
        "\n",
        "  f = line.find('clip-path')\n",
        "  if (f < 0): return line\n",
        "  fc = line.find('\"', f) + 1\n",
        "  fe = line.find('\"', fc) +1\n",
        "  return line[:f]+line[fe:]\n",
        "\n",
        "def fixup_svg(infile):\n",
        "  global indef\n",
        "  indef = False\n",
        "  outfile = \"kt_\"+ infile\n",
        "  replace_list = [['fill:none;',\"\"], ['style=\"fill:#ffffff;\"/>','style=\"fill:none;stroke:#000000\"/>' ]]\n",
        "  with open(infile) as fin, open(outfile, \"w+\") as fout:\n",
        "    for line in fin:\n",
        "      line = rm_clippath(line)\n",
        "      for pair in replace_list:\n",
        "        line = line.replace(pair[0], pair[1])\n",
        "      fout.write(line)\n",
        "  return outfile\n",
        "\n",
        "def save_fig(name):\n",
        "#  plt.axis('equal') # sometimes you need this but you can put it before save_fig\n",
        "  plt.axis('off')\n",
        "  plt.savefig(name + \".svg\", bbox_inches = 'tight')\n",
        "  outputfilename = fixup_svg(name + \".svg\")\n",
        "  files.download(outputfilename)"
      ],
      "metadata": {
        "id": "q_XWgPE536fO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "I want a signal that is a sine wave inside a gassian. This turns out not to have any application yet but it would make the center open and harder to fold with the edges compressible, like a wrapper on a candy."
      ],
      "metadata": {
        "id": "biQc1ZgRyBug"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "edge = 0.6\n",
        "amplitude = 0.3\n",
        "download = False\n",
        "\n",
        "t = np.linspace(-edge, edge, 2 * 100, endpoint=False)\n",
        "i, q, e = signal.gausspulse(t, fc=5, retquad=True, retenv=True)\n",
        "x = amplitude * i\n",
        "plt.plot(t, x)\n",
        "\n",
        "plt.axis('equal')\n",
        "plt.axis('off')\n",
        "\n",
        "name = \"gausspulse\"\n",
        "plt.savefig(name + \".svg\")\n",
        "outputfilename = fixup_svg(name + \".svg\")\n",
        "if (download): files.download(outputfilename)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "qANgG9m44Djx",
        "outputId": "0c566bdd-c902-4b32-9dc0-413188855444"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Chirps are kind of the opposide of a sine-contained-in-a-gaussian. These have a lot of applications in my origami as (when mirrored) they make the center very compressible (and rotatable) but the edges are curvy and fixed. \n",
        "\n",
        "To make a foldable origami from this, take the SVG and replicate it several times. A smaller amplitude is likely to work best but I tend to do that as I build the project. Here is a [Cricut Project.](https://design.cricut.com/landing/project-detail/637b9916f431d6b2923ef566) with pictures of partially complete and the full rotation and compression."
      ],
      "metadata": {
        "id": "qlYcPg6PyBK2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "t = np.linspace(0, 5, 500)\n",
        "\n",
        "wq = signal.chirp(t, f0=0.1, f1=1, t1=5, method='quadratic')\n",
        "plt.plot(t, wq)\n",
        "if (download): save_fig(\"chirp01_1_quadratic\")"
      ],
      "metadata": {
        "id": "LtlHnw9qEZ1r",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "c5df6f8a-ce21-4e63-94c5-3e7ecca0fa7d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "t = np.linspace(0, 5, 500)\n",
        "\n",
        "wh = signal.chirp(t, f0=0.1, f1=1, t1=5, method='hyperbolic')\n",
        "plt.plot(t, wh)\n",
        "if (download): save_fig(\"chirp01_1_hyperbolic\")"
      ],
      "metadata": {
        "id": "P40wal4o4QJk",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "9f06182d-94d9-40a7-c557-f75602b47843"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "The next function rotates a signal around a point. This is usually added to a new signal."
      ],
      "metadata": {
        "id": "zdQr4sbPelB0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def rotate(p, origin=(0, 0), degrees=0):\n",
        "    angle = np.deg2rad(degrees)\n",
        "    R = np.array([[np.cos(angle), -np.sin(angle)],\n",
        "                  [np.sin(angle),  np.cos(angle)]])\n",
        "    o = np.atleast_2d(origin)\n",
        "    p = np.atleast_2d(p)\n",
        "    return np.squeeze((R @ (p.T-o.T) + o.T).T)"
      ],
      "metadata": {
        "id": "oTI3azIgsGIY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Below is a nice wave pattern, generated from chirps rotated around point that is off screen. Note that this clips the signal so it fits in a particular frame. This pattern works well in the Origami Simulator. Here is a [Cricut Project](https://design.cricut.com/landing/project-detail/63a2771bb3466a71efaf57aa) with a pic and the pattern imported."
      ],
      "metadata": {
        "id": "OA48Gjhfzw-M"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "t = np.linspace(-1, 8, 500)\n",
        "y2 =5/((t+3))\n",
        "wl = 0.5*signal.chirp(t, f0=0.1, f1=1, t1=6, method='linear')\n",
        "\n",
        "falling_chirp= wl*y2\n",
        "\n",
        "xr = np.hstack((np.vstack(t), np.vstack(falling_chirp)))\n",
        "origin=(xr[0])\n",
        "xr = rotate(xr, origin=origin, degrees=30)\n",
        "total_angle = 0\n",
        "angle = 10\n",
        "color = 'b'\n",
        "while (total_angle <= 80):\n",
        "  if color == 'b':\n",
        "    color = 'r'\n",
        "  else:\n",
        "    color = 'b'\n",
        "  xr = rotate(xr, origin=origin, degrees=-angle)\n",
        "  plt.plot(xr[:,0], xr[:, 1], color) \n",
        "  total_angle += angle\n",
        "\n",
        "print(origin)\n",
        "plt.axis('equal')\n",
        "plt.ylim([-2.15, 0.85])\n",
        "plt.xlim([-0.7, 5.3])\n",
        "plt.axis('off')\n",
        "#plt.axis('on')\n",
        "if (download): save_fig(\"waves1\")\n",
        "# This turns out pretty good, a lot of stress around that first sharp turn but \n",
        "# overall, very nice"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 266
        },
        "id": "DoLdIcaGtSe9",
        "outputId": "7f737913-f9c4-4c37-f577-4e542d82ebec"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[-1.          1.23461043]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following pattern is NOT good, too much interference between the straights and curves. "
      ],
      "metadata": {
        "id": "76E4uWKJ0LDC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Another take on waves\n",
        "\n",
        "t = np.linspace(-1, 8, 500)\n",
        "y2 =5/((t+3))\n",
        "wl = 0.25*signal.chirp(t, f0=0.1, f1=1, t1=6, method='linear')\n",
        "\n",
        "falling_chirp= wl*y2\n",
        "\n",
        "xr = np.hstack((np.vstack(t), np.vstack(falling_chirp)))\n",
        "origin=(xr[0])\n",
        "xr = rotate(xr, origin=origin, degrees=30)\n",
        "total_angle = 0\n",
        "angle = 5\n",
        "color = 'b'\n",
        "while (total_angle <= 80):\n",
        "  if color == 'b':\n",
        "    color = 'r'\n",
        "  else:\n",
        "    color = 'b'\n",
        "  xr[:,1] = xr[:,1] - 0.1\n",
        "  origin=(xr[0])\n",
        "  xr = rotate(xr, origin=origin, degrees=-angle)\n",
        "  plt.plot(xr[:,0], xr[:, 1], color) \n",
        "  total_angle += angle\n",
        "\n",
        "  \n",
        "plt.axis('equal')\n",
        "plt.ylim([-2.5, 0.5])\n",
        "plt.xlim([0, 6])\n",
        "plt.axis('off')\n",
        "#plt.axis('on')\n",
        "if (download): save_fig(\"waves2\")\n",
        "# This is not as good as previous, the sine areas fight each other"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "Pt_uPwkH5brt",
        "outputId": "776861c1-16a2-4355-d640-0c0318a2afd4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Sine waves that move in different ways are interesting. This has a sine wave added to a binomial as I started to explore sine waves of sine waves. This didn't turn out to have a lot of utility but I do have a nice [Cricut Project](https://design.cricut.com/landing/project-detail/631256e2fc3f79a4ca39b3f2) of simple sine waves."
      ],
      "metadata": {
        "id": "MEGasy8U3cUC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Define the x-values for the two signals\n",
        "x = np.linspace(-2*np.pi, 2*np.pi, 500)\n",
        "\n",
        "# Define the two signals\n",
        "y1 = np.sin(4*x)\n",
        "y2 =(1/5)* x**2\n",
        "\n",
        "# add them together\n",
        "y3 = y1+y2\n",
        "\n",
        "# Plot the resulting signal\n",
        "plt.plot(x, y1, 'r', x, y2,'b', x, y3, 'g')\n",
        "if (download): save_fig(\"sin4x_plus_02xsq\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "Wxppe0tVL8Gl",
        "outputId": "d40323c7-670e-4e66-ba26-38e397d205f3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ],
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ],
            "application/javascript": [
              "download(\"download_fa08769a-f217-48e4-860d-97875fb4eb06\", \"kt_sin4x_plus_02xsq.svg\", 15532)"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Bezier output \n",
        "!pip install svgpathtools\n",
        "import svgpathtools\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NbYyuYqzENVF",
        "outputId": "73b90cd0-ccb7-4c73-bf63-751a621fcdff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting svgpathtools\n",
            "  Downloading svgpathtools-1.6.0-py2.py3-none-any.whl (67 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m67.4/67.4 KB\u001b[0m \u001b[31m6.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: numpy in /usr/local/lib/python3.8/dist-packages (from svgpathtools) (1.21.6)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.8/dist-packages (from svgpathtools) (1.7.3)\n",
            "Collecting svgwrite\n",
            "  Downloading svgwrite-1.4.3-py3-none-any.whl (67 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m67.1/67.1 KB\u001b[0m \u001b[31m6.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hInstalling collected packages: svgwrite, svgpathtools\n",
            "Successfully installed svgpathtools-1.6.0 svgwrite-1.4.3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from svgpathtools import svg2paths2\n",
        "from svgpathtools import smoothed_path\n",
        "import svgpathtools\n",
        "\n",
        "paths, attributes, svg_attributes = svg2paths2('sin4x_plus_02xsq.svg')"
      ],
      "metadata": {
        "id": "5r2xYUVVEiyz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "print(\"Starting: {} paths\", len(paths))\n",
        "for i in range(len(paths)):\n",
        "  if 'style' in attributes[i]:\n",
        "    print(\"  {}  len {} style {}\".format(i, len(paths[i]), attributes[i]['style']))\n",
        "  else:\n",
        "    print(\"  {}  len {} \".format(i, len(paths[i])))\n",
        "#  s = smoothed_path(paths[i])\n",
        "#  print(\"    smoothed  len {} \".format(i, len(s)))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tpOmBi-VG1rS",
        "outputId": "5c3461cf-a4bd-4600-8781-c6a0e7018bba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Starting: {} paths 5\n",
            "  0  len 4 style fill:#ffffff;\n",
            "  1  len 263 style fill:none;stroke:#ff0000;stroke-linecap:square;stroke-width:1.5;\n",
            "  2  len 66 style fill:none;stroke:#0000ff;stroke-linecap:square;stroke-width:1.5;\n",
            "  3  len 264 style fill:none;stroke:#008000;stroke-linecap:square;stroke-width:1.5;\n",
            "  4  len 4 \n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# for each path whose len >4\n",
        "  # for each Line in the path\n",
        "    # points.append( [line.start.real , line.start.imag])\n",
        "    # if current.end != next.end\n",
        "      # points.append(end)\n",
        "  # feed the data into get_bezier_parameters\n",
        "  # create a Quadratic Bezier with svgpathtools\n",
        "  # wsvg on output\n",
        "\n",
        "data = get_bezier_parameters(xpoints, ypoints, degree=4)\n",
        "x_val = [x[0] for x in data]\n",
        "y_val = [x[1] for x in data]\n",
        "\n",
        "xvals, yvals = bezier_curve(data, nTimes=1000)\n",
        "plt.plot(xvals, yvals, 'b-', label='B Curve')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e4cRTfjbHPs0",
        "outputId": "6a1bad58-307b-47a7-dde2-07325e2a84be"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(22.418182+22.024578j)"
            ]
          },
          "metadata": {},
          "execution_count": 130
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "LtxB79eiIGEq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "s = smoothed_path(paths[2])\n",
        "print(len(s), len(paths[2]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hmo96cD5NWYw",
        "outputId": "9fecbee5-f604-49a9-9a41-025713e2f317"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "129 65\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "p = 3\n",
        "for i in range(len(paths[p])):\n",
        "  if paths[p][i].start == paths[p][i].end:\n",
        "      print(i)\n",
        "      paths[p].remove(paths[p][i])\n"
      ],
      "metadata": {
        "id": "wEdZZnNXNsuH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#https://stackoverflow.com/questions/12643079/bézier-curve-fitting-with-scipy\n",
        "\n",
        "import numpy as np\n",
        "from scipy.special import comb\n",
        "\n",
        "def get_bezier_parameters(X, Y, degree=3):\n",
        "    \"\"\" Least square qbezier fit using penrose pseudoinverse.\n",
        "\n",
        "    Parameters:\n",
        "\n",
        "    X: array of x data.\n",
        "    Y: array of y data. Y[0] is the y point for X[0].\n",
        "    degree: degree of the Bézier curve. 2 for quadratic, 3 for cubic.\n",
        "\n",
        "    Based on https://stackoverflow.com/questions/12643079/b%C3%A9zier-curve-fitting-with-scipy\n",
        "    and probably on the 1998 thesis by Tim Andrew Pastva, \"Bézier Curve Fitting\".\n",
        "    \"\"\"\n",
        "    if degree < 1:\n",
        "        raise ValueError('degree must be 1 or greater.')\n",
        "\n",
        "    if len(X) != len(Y):\n",
        "        raise ValueError('X and Y must be of the same length.')\n",
        "\n",
        "    if len(X) < degree + 1:\n",
        "        raise ValueError(f'There must be at least {degree + 1} points to '\n",
        "                         f'determine the parameters of a degree {degree} curve. '\n",
        "                         f'Got only {len(X)} points.')\n",
        "\n",
        "    def bpoly(n, t, k):\n",
        "        \"\"\" Bernstein polynomial when a = 0 and b = 1. \"\"\"\n",
        "        return t ** k * (1 - t) ** (n - k) * comb(n, k)\n",
        "        #return comb(n, i) * ( t**(n-i) ) * (1 - t)**i\n",
        "\n",
        "    def bmatrix(T):\n",
        "        \"\"\" Bernstein matrix for Bézier curves. \"\"\"\n",
        "        return np.matrix([[bpoly(degree, t, k) for k in range(degree + 1)] for t in T])\n",
        "\n",
        "    def least_square_fit(points, M):\n",
        "        M_ = np.linalg.pinv(M)\n",
        "        return M_ * points\n",
        "\n",
        "    T = np.linspace(0, 1, len(X))\n",
        "    M = bmatrix(T)\n",
        "    points = np.array(list(zip(X, Y)))\n",
        "    \n",
        "    final = least_square_fit(points, M).tolist()\n",
        "    final[0] = [X[0], Y[0]]\n",
        "    final[len(final)-1] = [X[len(X)-1], Y[len(Y)-1]]\n",
        "    return final\n",
        "def bernstein_poly(i, n, t):\n",
        "    \"\"\"\n",
        "     The Bernstein polynomial of n, i as a function of t\n",
        "    \"\"\"\n",
        "    return comb(n, i) * ( t**(n-i) ) * (1 - t)**i\n",
        "\n",
        "\n",
        "def bezier_curve(points, nTimes=50):\n",
        "    \"\"\"\n",
        "       Given a set of control points, return the\n",
        "       bezier curve defined by the control points.\n",
        "\n",
        "       points should be a list of lists, or list of tuples\n",
        "       such as [ [1,1], \n",
        "                 [2,3], \n",
        "                 [4,5], ..[Xn, Yn] ]\n",
        "        nTimes is the number of time steps, defaults to 1000\n",
        "\n",
        "        See http://processingjs.nihongoresources.com/bezierinfo/\n",
        "    \"\"\"\n",
        "\n",
        "    nPoints = len(points)\n",
        "    xPoints = np.array([p[0] for p in points])\n",
        "    yPoints = np.array([p[1] for p in points])\n",
        "\n",
        "    t = np.linspace(0.0, 1.0, nTimes)\n",
        "\n",
        "    polynomial_array = np.array([ bernstein_poly(i, nPoints-1, t) for i in range(0, nPoints)   ])\n",
        "\n",
        "    xvals = np.dot(xPoints, polynomial_array)\n",
        "    yvals = np.dot(yPoints, polynomial_array)\n",
        "\n",
        "    return xvals, yvals\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "gYItiOFsN-lb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "points = []\n",
        "xpoints = [19.21270, 19.21269, 19.21268, 19.21266, 19.21264, 19.21263, 19.21261, 19.21261, 19.21264, 19.21268,19.21274, 19.21282, 19.21290, 19.21299, 19.21307, 19.21316, 19.21324, 19.21333, 19.21342]\n",
        "ypoints = [-100.14895, -100.14885, -100.14875, -100.14865, -100.14855, -100.14847, -100.14840, -100.14832, -100.14827, -100.14823, -100.14818, -100.14818, -100.14818, -100.14818, -100.14819, -100.14819, -100.14819, -100.14820, -100.14820]\n",
        "for i in range(len(xpoints)):\n",
        "    points.append([xpoints[i],ypoints[i]])"
      ],
      "metadata": {
        "id": "3-xRU8bBTRXe"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "# Plot the original points\n",
        "plt.plot(xpoints, ypoints, \"ro\",label='Original Points')\n",
        "# Get the Bezier parameters based on a degree.\n",
        "data = get_bezier_parameters(xpoints, ypoints, degree=4)\n",
        "x_val = [x[0] for x in data]\n",
        "y_val = [x[1] for x in data]\n",
        "print(data)\n",
        "# Plot the control points\n",
        "plt.plot(x_val,y_val,'k--o', label='Control Points')\n",
        "# Plot the resulting Bezier curve\n",
        "xvals, yvals = bezier_curve(data, nTimes=1000)\n",
        "plt.plot(xvals, yvals, 'b-', label='B Curve')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 327
        },
        "id": "D0YDIx6lTXMp",
        "outputId": "784ebb69-64ee-48cd-8409-08251e4f2543"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[19.2127, -100.14895], [19.21269253408782, -100.14851871628683], [19.212244684681664, -100.14789676091237], [19.213163415737142, -100.14825934814728], [19.21342, -100.1482]]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(len(xpoints), len(x_val), len(xvals))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1SG83K77TY81",
        "outputId": "a83509fe-41bc-496d-c2f5-139ba341e121"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "19 5 1000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(x_val)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ilV8r2ghXVKn",
        "outputId": "eaffbbb8-f58b-402f-e04b-f3e9064c2e52"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[19.2127, 19.21269253408782, 19.212244684681664, 19.213163415737142, 19.21342]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(y_val)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z1Phz2v2YuHO",
        "outputId": "2fff863b-c1bf-4166-d029-8ebdfc6ff9ff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[-100.14895, -100.14851871628683, -100.14789676091237, -100.14825934814728, -100.1482]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(data)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ycw3ZMlSY0Rx",
        "outputId": "04db128e-706a-4e49-8545-febe3b52b94f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[19.2127, -100.14895], [19.21269253408782, -100.14851871628683], [19.212244684681664, -100.14789676091237], [19.213163415737142, -100.14825934814728], [19.21342, -100.1482]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "TvUETkLbY2CK"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}