├── .gitignore ├── COPYING ├── README ├── canvas3d.py ├── doc └── sphinx │ ├── Makefile │ ├── canvas3d.rst │ ├── conf.py │ ├── index.rst │ ├── math3d.rst │ └── scene.rst ├── math3d.py ├── neat_demo.py └── scene.py /.gitignore: -------------------------------------------------------------------------------- 1 | *.pyc 2 | *.pyo 3 | _build/ 4 | -------------------------------------------------------------------------------- /COPYING: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README: -------------------------------------------------------------------------------- 1 | This is a simple 3D math module and some code that uses it to render objects in a 2 | Tkinter Canvas and move them around in 3D. 3 | 4 | It's still in a rough state, although it works. I'll clean it up. 5 | 6 | There's no installation. Simply change into the directory and run the 7 | neat_demo.py script to try it out. This will open a Tk window and draw a 8 | rotating cube. Woo! 9 | 10 | Please send questions or comments to the author at sforman@hushmail.com 11 | 12 | 13 | Copyright 2011, 2012, 2013, 2014 Simon Forman 14 | 15 | Tkinter3D is free software: you can redistribute it and/or modify 16 | it under the terms of the GNU General Public License as published by 17 | the Free Software Foundation, either version 3 of the License, or 18 | (at your option) any later version. 19 | 20 | Tkinter3D is distributed in the hope that it will be useful, 21 | but WITHOUT ANY WARRANTY; without even the implied warranty of 22 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 23 | GNU General Public License for more details. 24 | 25 | You should have received a copy of the GNU General Public License 26 | along with Tkinter3D. If not, see . 27 | -------------------------------------------------------------------------------- /canvas3d.py: -------------------------------------------------------------------------------- 1 | # 2 | # Copyright 2011, 2012, 2013, 2014 Simon Forman 3 | # 4 | # This file is part of Tkinter3D. 5 | # 6 | # Tkinter3D is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # 11 | # Tkinter3D is distributed in the hope that it will be useful, 12 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 13 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 | # GNU General Public License for more details. 15 | # 16 | # You should have received a copy of the GNU General Public License 17 | # along with Tkinter3D. If not, see . 18 | # 19 | ''' 20 | A Docstring for canvas3d module. 21 | ''' 22 | from tkinter import Tk, Canvas 23 | from math3d import ( 24 | Vector, 25 | planeNormalAndDistance, 26 | rotx, 27 | roty, 28 | rotz, 29 | radians, 30 | ) 31 | from math import tan, pi 32 | from scene import Frame3D 33 | 34 | 35 | def G(L, a): 36 | return L / tan(a / radians) #the arc of the viewport 37 | 38 | 39 | class Canvas3D(Canvas): 40 | ''' 41 | A Tkinter Canvas adapted to serve as a 3D viewer. 42 | ''' 43 | 44 | def __init__(self, master=None, fps=20, *args, **kw): 45 | Canvas.__init__(self, master, *args, **kw) 46 | 47 | self.frame = Frame3D() 48 | self.items = {} 49 | 50 | self.w = float(self['width']) 51 | self.h = float(self['height']) 52 | 53 | self.axes_on = True 54 | self._xy_axes() 55 | 56 | self.bind('', self.resize_callback) 57 | 58 | self.fps_ms = 1000 / fps # Frames per second in milliseconds. 59 | 60 | self.focal_distance = 2.2 61 | self.x_arc_of_view = 73.0 62 | self.y_arc_of_view = 73.0 63 | 64 | self.f = G(self.w, self.x_arc_of_view) 65 | self.u = G(self.h, self.y_arc_of_view) 66 | 67 | self._frustum = Frustum( 68 | self.w, 69 | self.h, 70 | self.x_arc_of_view, 71 | self.y_arc_of_view, 72 | self.focal_distance, 73 | ) 74 | 75 | def visible(self, v): 76 | ''' 77 | Return a Boolean indicating if the given Vector is within the 78 | view. 79 | 80 | :param v: A Vector representing a 3D point. 81 | :type v: :class:`math3d.Vector` 82 | :rtype: Boolean 83 | 84 | ''' 85 | return self._frustum.visible(v) 86 | 87 | def vector_to_screen(self, v): 88 | ''' 89 | Return X and Y coordinates of Vector v projected onto the screen 90 | space. 91 | 92 | :param v: A Vector representing a 3D point. 93 | :type v: :class:`math3d.Vector` 94 | :returns: X, Y coordinates on Canvas. 95 | :rtype: two-tuple of :obj:`int` 96 | 97 | ''' 98 | z = v.z 99 | FD = self.focal_distance 100 | w = self.w / 2 101 | f = self.f 102 | h = self.h / 2 103 | u = self.u 104 | 105 | return ( 106 | int(w + v.x * f / (z + f * FD)), 107 | int(h - v.y * u / (z + u * FD)) 108 | ) 109 | 110 | def _xy_axes(self): 111 | if not self.axes_on: 112 | return 113 | 114 | w, h = int(self.w), int(self.h) 115 | 116 | yaxis = self.items.get('yaxis', None) 117 | if yaxis: 118 | self.coords(yaxis, w / 2, 0, w / 2, h) 119 | else: 120 | self.items['yaxis'] = self.create_line(w / 2, 0, w / 2, h) 121 | 122 | xaxis = self.items.get('xaxis', None) 123 | if xaxis: 124 | self.coords(xaxis, w, h / 2, 0, h / 2) 125 | else: 126 | self.items['xaxis'] = self.create_line(w, h / 2, 0, h / 2) 127 | 128 | def resize_callback(self, event): 129 | self.w = float(event.width) 130 | self.h = float(event.height) 131 | self._xy_axes() 132 | 133 | def start_updating(self): 134 | self._updater() 135 | 136 | def _updater(self): 137 | self.do_frame() 138 | self.update_idletasks() 139 | self.update() 140 | self.after(int(self.fps_ms), self._updater) 141 | 142 | def do_frame(self): 143 | for thing, vector in self.frame.yieldTransformed(): 144 | 145 | if self._frustum.visible(vector): 146 | x, y = self.vector_to_screen(vector) 147 | thing.render(x, y, 1.0) 148 | 149 | else: 150 | thing.hide() 151 | 152 | 153 | class Frustum: 154 | 155 | def __init__( 156 | self, 157 | width=320, 158 | height=240, 159 | x_arc=73.0, 160 | y_arc=73.0, 161 | focal_distance=2.2, 162 | depth=5000.0, 163 | ): 164 | 165 | self.w, self.h = width, height 166 | self.xarc, self.yarc = x_arc, y_arc 167 | self.FD = focal_distance 168 | self.depth = depth 169 | 170 | self.T = Vector() 171 | self.RM = rotx(0) * roty(0) * rotz(0) 172 | 173 | # Create a list of eight "blank" new Vectors. These will be the 174 | # corners of the frustum, used to determine the planes beyond 175 | # which a given point is outside the viewable space. 176 | self._frustum = [Vector() for _ in range(8)] 177 | 178 | self._reset() 179 | self._getFrustumPlanes() 180 | 181 | def _reset(self): 182 | self.f = G(self.w, self.xarc) 183 | self.u = G(self.h, self.yarc) 184 | self._frustum_dirty = True 185 | self._frustum_planes_dirty = True 186 | 187 | def transform(self, v): 188 | return (v - self.T) * self.RM 189 | 190 | def visible(self, v): 191 | """ 192 | Is vector v in World coordinates within the view frustum? 193 | """ 194 | (lpN, ld), (rpN, rd), (tpN, td), (bpN, bd) = self._getFrustumPlanes() 195 | vx, vy, vz = v.x, v.y, v.z 196 | accs = acl, acr, act, acb = -ld, -rd, -td, -bd 197 | 198 | if vx != 0.0: 199 | acl += vx * lpN.x 200 | acr += vx * rpN.x 201 | act += vx * tpN.x 202 | acb += vx * bpN.x 203 | 204 | if vy != 0.0: 205 | acl += vy * lpN.y 206 | acr += vy * rpN.y 207 | act += vy * tpN.y 208 | acb += vy * bpN.y 209 | 210 | if vz != 0.0: 211 | if ( 212 | (acl + vz * lpN.z <= 0.0) 213 | or (acr + vz * rpN.z <= 0.0) 214 | or (act + vz * tpN.z <= 0.0) 215 | ): 216 | return False 217 | return acb + vz * bpN.z > 0.0 218 | 219 | if acl <= 0.0 or acr <= 0.0 or act <= 0.0: 220 | return False 221 | return acb > 0.0 222 | 223 | def _getFrustum(self): 224 | """ 225 | This returns the coordinates of the view frustum in self/model 226 | coordinates. 227 | """ 228 | if self._frustum_dirty: 229 | FD, w, h, f, u = self.FD, self.w, self.h, self.f, self.u 230 | v0, v1, v2, v3, v4, v5, v6, v7 = self._frustum 231 | z = min(f, u) 232 | 233 | xw = w / 2.0 * (z + f * FD) / f 234 | x0 = -xw 235 | yh = h / 2.0 * (z + u * FD) / u 236 | y0 = -yh 237 | 238 | v0.x, v0.y, v0.z = x0, y0, z 239 | v1.x, v1.y, v1.z = xw, yh, z 240 | v2.x, v2.y, v2.z = xw, y0, z 241 | v3.x, v3.y, v3.z = x0, yh, z 242 | 243 | z = self.depth 244 | xw = w / 2.0 * (z + f * FD) / f 245 | x0 = -xw 246 | yh = h / 2.0 * (z + u * FD) / u 247 | y0 = -yh 248 | 249 | v4.x, v4.y, v4.z = x0, y0, z 250 | v5.x, v5.y, v5.z = xw, yh, z 251 | v6.x, v6.y, v6.z = xw, y0, z 252 | v7.x, v7.y, v7.z = x0, yh, z 253 | 254 | self._frustum_dirty = False 255 | 256 | return self._frustum 257 | 258 | def _getFrustumPlanes(self): 259 | if self._frustum_planes_dirty: 260 | 261 | V = list(map(self.transform, self._getFrustum())) 262 | self._frustum_planes = tuple( 263 | planeNormalAndDistance(V[i0], V[i1], V[i2]) 264 | for i0, i1, i2 in ( 265 | (0, 4, 3), 266 | (6, 2, 5), 267 | (3, 7, 1), 268 | (2, 6, 0), 269 | ) 270 | ) 271 | self._frustum_planes_dirty = False 272 | 273 | return self._frustum_planes 274 | 275 | 276 | if __name__ == '__main__': 277 | from scene import Thing3D as dot 278 | 279 | root = Tk() 280 | root.title("Rotating Cube Demo") 281 | c = Canvas3D(root) 282 | c.pack(expand=1, fill='both') 283 | 284 | ## Changing the frustum's "frame". 285 | # c._frustum.T.z += 100.0 286 | # c._frustum._reset() 287 | 288 | # Zoom out a little. 289 | c.frame.T.z += -200.0 290 | 291 | # Create a dot at world origin (0, 0, 0). 292 | origin = dot(c) 293 | c.frame.things.append(origin) 294 | 295 | # Make a cube. 296 | cube_frame = Frame3D() 297 | c.frame.subframes.append(cube_frame) 298 | coords = -1, 1 299 | for x in coords: 300 | for y in coords: 301 | for z in coords: 302 | d = dot(c, 100.0 * x, 100.0 * y, 100.0 * z) 303 | cube_frame.things.append(d) 304 | 305 | # Apply a rotation repeatedly to our cube. 306 | N = roty(360/30/3) # 4 degrees. 307 | def delta(): 308 | cube_frame.RM *= N 309 | c.after(60, delta) 310 | 311 | # Start everything running. 312 | delta() 313 | c.start_updating() 314 | root.mainloop() 315 | -------------------------------------------------------------------------------- /doc/sphinx/Makefile: -------------------------------------------------------------------------------- 1 | # Makefile for Sphinx documentation 2 | # 3 | 4 | # You can set these variables from the command line. 5 | SPHINXOPTS = 6 | SPHINXBUILD = sphinx-build 7 | PAPER = 8 | BUILDDIR = _build 9 | 10 | # Internal variables. 11 | PAPEROPT_a4 = -D latex_paper_size=a4 12 | PAPEROPT_letter = -D latex_paper_size=letter 13 | ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) . 14 | 15 | .PHONY: help clean html dirhtml pickle json htmlhelp qthelp latex changes linkcheck doctest 16 | 17 | help: 18 | @echo "Please use \`make ' where is one of" 19 | @echo " html to make standalone HTML files" 20 | @echo " dirhtml to make HTML files named index.html in directories" 21 | @echo " pickle to make pickle files" 22 | @echo " json to make JSON files" 23 | @echo " htmlhelp to make HTML files and a HTML help project" 24 | @echo " qthelp to make HTML files and a qthelp project" 25 | @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter" 26 | @echo " changes to make an overview of all changed/added/deprecated items" 27 | @echo " linkcheck to check all external links for integrity" 28 | @echo " doctest to run all doctests embedded in the documentation (if enabled)" 29 | 30 | clean: 31 | -rm -rf $(BUILDDIR)/* 32 | 33 | html: 34 | $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html 35 | @echo 36 | @echo "Build finished. The HTML pages are in $(BUILDDIR)/html." 37 | 38 | dirhtml: 39 | $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml 40 | @echo 41 | @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml." 42 | 43 | pickle: 44 | $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle 45 | @echo 46 | @echo "Build finished; now you can process the pickle files." 47 | 48 | json: 49 | $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json 50 | @echo 51 | @echo "Build finished; now you can process the JSON files." 52 | 53 | htmlhelp: 54 | $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp 55 | @echo 56 | @echo "Build finished; now you can run HTML Help Workshop with the" \ 57 | ".hhp project file in $(BUILDDIR)/htmlhelp." 58 | 59 | qthelp: 60 | $(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp 61 | @echo 62 | @echo "Build finished; now you can run "qcollectiongenerator" with the" \ 63 | ".qhcp project file in $(BUILDDIR)/qthelp, like this:" 64 | @echo "# qcollectiongenerator $(BUILDDIR)/qthelp/Tkinter3D.qhcp" 65 | @echo "To view the help file:" 66 | @echo "# assistant -collectionFile $(BUILDDIR)/qthelp/Tkinter3D.qhc" 67 | 68 | latex: 69 | $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex 70 | @echo 71 | @echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex." 72 | @echo "Run \`make all-pdf' or \`make all-ps' in that directory to" \ 73 | "run these through (pdf)latex." 74 | 75 | changes: 76 | $(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes 77 | @echo 78 | @echo "The overview file is in $(BUILDDIR)/changes." 79 | 80 | linkcheck: 81 | $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck 82 | @echo 83 | @echo "Link check complete; look for any errors in the above output " \ 84 | "or in $(BUILDDIR)/linkcheck/output.txt." 85 | 86 | doctest: 87 | $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest 88 | @echo "Testing of doctests in the sources finished, look at the " \ 89 | "results in $(BUILDDIR)/doctest/output.txt." 90 | -------------------------------------------------------------------------------- /doc/sphinx/canvas3d.rst: -------------------------------------------------------------------------------- 1 | 2 | :mod:`canvas3d` -- Tkinter Canvas to Display 3D Entities 3 | ======================================================== 4 | 5 | .. automodule:: canvas3d 6 | 7 | 8 | .. autoclass:: Canvas3D 9 | :members: 10 | :undoc-members: 11 | 12 | -------------------------------------------------------------------------------- /doc/sphinx/conf.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | # 3 | # Tkinter3D documentation build configuration file, created by 4 | # sphinx-quickstart on Tue Jul 26 19:37:44 2011. 5 | # 6 | # This file is execfile()d with the current directory set to its containing dir. 7 | # 8 | # Note that not all possible configuration values are present in this 9 | # autogenerated file. 10 | # 11 | # All configuration values have a default; values that are commented out 12 | # serve to show the default. 13 | 14 | import sys, os 15 | 16 | # If extensions (or modules to document with autodoc) are in another directory, 17 | # add these directories to sys.path here. If the directory is relative to the 18 | # documentation root, use os.path.abspath to make it absolute, like shown here. 19 | 20 | sys.path.append(os.path.abspath('../..')) 21 | 22 | # -- General configuration ----------------------------------------------------- 23 | 24 | # Add any Sphinx extension module names here, as strings. They can be extensions 25 | # coming with Sphinx (named 'sphinx.ext.*') or your custom ones. 26 | extensions = ['sphinx.ext.autodoc', 'sphinx.ext.todo', 'sphinx.ext.coverage'] 27 | 28 | # Add any paths that contain templates here, relative to this directory. 29 | templates_path = ['_templates'] 30 | 31 | # The suffix of source filenames. 32 | source_suffix = '.rst' 33 | 34 | # The encoding of source files. 35 | #source_encoding = 'utf-8' 36 | 37 | # The master toctree document. 38 | master_doc = 'index' 39 | 40 | # General information about the project. 41 | project = u'Tkinter3D' 42 | copyright = u'2011, Simon Forman' 43 | 44 | # The version info for the project you're documenting, acts as replacement for 45 | # |version| and |release|, also used in various other places throughout the 46 | # built documents. 47 | # 48 | # The short X.Y version. 49 | version = '0.1' 50 | # The full version, including alpha/beta/rc tags. 51 | release = '0.1' 52 | 53 | # The language for content autogenerated by Sphinx. Refer to documentation 54 | # for a list of supported languages. 55 | #language = None 56 | 57 | # There are two options for replacing |today|: either, you set today to some 58 | # non-false value, then it is used: 59 | #today = '' 60 | # Else, today_fmt is used as the format for a strftime call. 61 | #today_fmt = '%B %d, %Y' 62 | 63 | # List of documents that shouldn't be included in the build. 64 | #unused_docs = [] 65 | 66 | # List of directories, relative to source directory, that shouldn't be searched 67 | # for source files. 68 | exclude_trees = ['_build'] 69 | 70 | # The reST default role (used for this markup: `text`) to use for all documents. 71 | #default_role = None 72 | 73 | # If true, '()' will be appended to :func: etc. cross-reference text. 74 | #add_function_parentheses = True 75 | 76 | # If true, the current module name will be prepended to all description 77 | # unit titles (such as .. function::). 78 | #add_module_names = True 79 | 80 | # If true, sectionauthor and moduleauthor directives will be shown in the 81 | # output. They are ignored by default. 82 | #show_authors = False 83 | 84 | # The name of the Pygments (syntax highlighting) style to use. 85 | pygments_style = 'sphinx' 86 | 87 | # A list of ignored prefixes for module index sorting. 88 | #modindex_common_prefix = [] 89 | 90 | 91 | # -- Options for HTML output --------------------------------------------------- 92 | 93 | # The theme to use for HTML and HTML Help pages. Major themes that come with 94 | # Sphinx are currently 'default' and 'sphinxdoc'. 95 | html_theme = 'default' 96 | 97 | # Theme options are theme-specific and customize the look and feel of a theme 98 | # further. For a list of options available for each theme, see the 99 | # documentation. 100 | #html_theme_options = {} 101 | 102 | # Add any paths that contain custom themes here, relative to this directory. 103 | #html_theme_path = [] 104 | 105 | # The name for this set of Sphinx documents. If None, it defaults to 106 | # " v documentation". 107 | #html_title = None 108 | 109 | # A shorter title for the navigation bar. Default is the same as html_title. 110 | #html_short_title = None 111 | 112 | # The name of an image file (relative to this directory) to place at the top 113 | # of the sidebar. 114 | #html_logo = None 115 | 116 | # The name of an image file (within the static path) to use as favicon of the 117 | # docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 118 | # pixels large. 119 | #html_favicon = None 120 | 121 | # Add any paths that contain custom static files (such as style sheets) here, 122 | # relative to this directory. They are copied after the builtin static files, 123 | # so a file named "default.css" will overwrite the builtin "default.css". 124 | html_static_path = ['_static'] 125 | 126 | # If not '', a 'Last updated on:' timestamp is inserted at every page bottom, 127 | # using the given strftime format. 128 | #html_last_updated_fmt = '%b %d, %Y' 129 | 130 | # If true, SmartyPants will be used to convert quotes and dashes to 131 | # typographically correct entities. 132 | #html_use_smartypants = True 133 | 134 | # Custom sidebar templates, maps document names to template names. 135 | #html_sidebars = {} 136 | 137 | # Additional templates that should be rendered to pages, maps page names to 138 | # template names. 139 | #html_additional_pages = {} 140 | 141 | # If false, no module index is generated. 142 | #html_use_modindex = True 143 | 144 | # If false, no index is generated. 145 | #html_use_index = True 146 | 147 | # If true, the index is split into individual pages for each letter. 148 | #html_split_index = False 149 | 150 | # If true, links to the reST sources are added to the pages. 151 | #html_show_sourcelink = True 152 | 153 | # If true, an OpenSearch description file will be output, and all pages will 154 | # contain a tag referring to it. The value of this option must be the 155 | # base URL from which the finished HTML is served. 156 | #html_use_opensearch = '' 157 | 158 | # If nonempty, this is the file name suffix for HTML files (e.g. ".xhtml"). 159 | #html_file_suffix = '' 160 | 161 | # Output file base name for HTML help builder. 162 | htmlhelp_basename = 'Tkinter3Ddoc' 163 | 164 | 165 | # -- Options for LaTeX output -------------------------------------------------- 166 | 167 | # The paper size ('letter' or 'a4'). 168 | #latex_paper_size = 'letter' 169 | 170 | # The font size ('10pt', '11pt' or '12pt'). 171 | #latex_font_size = '10pt' 172 | 173 | # Grouping the document tree into LaTeX files. List of tuples 174 | # (source start file, target name, title, author, documentclass [howto/manual]). 175 | latex_documents = [ 176 | ('index', 'Tkinter3D.tex', u'Tkinter3D Documentation', 177 | u'Simon Forman', 'manual'), 178 | ] 179 | 180 | # The name of an image file (relative to this directory) to place at the top of 181 | # the title page. 182 | #latex_logo = None 183 | 184 | # For "manual" documents, if this is true, then toplevel headings are parts, 185 | # not chapters. 186 | #latex_use_parts = False 187 | 188 | # Additional stuff for the LaTeX preamble. 189 | #latex_preamble = '' 190 | 191 | # Documents to append as an appendix to all manuals. 192 | #latex_appendices = [] 193 | 194 | # If false, no module index is generated. 195 | #latex_use_modindex = True 196 | -------------------------------------------------------------------------------- /doc/sphinx/index.rst: -------------------------------------------------------------------------------- 1 | .. Tkinter3D documentation master file, created by 2 | sphinx-quickstart on Tue Jul 26 19:37:44 2011. 3 | You can adapt this file completely to your liking, but it should at least 4 | contain the root `toctree` directive. 5 | 6 | Welcome to Tkinter3D's documentation! 7 | ===================================== 8 | 9 | Contents: 10 | 11 | .. toctree:: 12 | :maxdepth: 2 13 | 14 | math3d 15 | scene 16 | canvas3d 17 | 18 | Indices and tables 19 | ================== 20 | 21 | * :ref:`genindex` 22 | * :ref:`modindex` 23 | * :ref:`search` 24 | 25 | -------------------------------------------------------------------------------- /doc/sphinx/math3d.rst: -------------------------------------------------------------------------------- 1 | 2 | :mod:`math3d` -- 3D Math 3 | ======================================================== 4 | 5 | .. automodule:: math3d 6 | 7 | .. autodata:: scalar_types 8 | 9 | .. autoclass:: Vector 10 | :members: 11 | :undoc-members: 12 | 13 | .. autoclass:: Matrix 14 | :members: 15 | :undoc-members: 16 | 17 | .. autoclass:: Quaternion 18 | :members: 19 | :undoc-members: 20 | 21 | 22 | -------------------------------------------------------------------------------- /doc/sphinx/scene.rst: -------------------------------------------------------------------------------- 1 | 2 | :mod:`scene` -- Support for 3D Scenes 3 | ======================================================== 4 | 5 | .. automodule:: scene 6 | 7 | .. autoclass:: Frame3D 8 | :members: 9 | 10 | .. autoclass:: Thing3D 11 | :members: 12 | :undoc-members: 13 | 14 | -------------------------------------------------------------------------------- /math3d.py: -------------------------------------------------------------------------------- 1 | # 2 | # Copyright 2011, 2012, 2013, 2014 Simon Forman 3 | # 4 | # This file is part of Tkinter3D. 5 | # 6 | # Tkinter3D is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # 11 | # Tkinter3D is distributed in the hope that it will be useful, 12 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 13 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 | # GNU General Public License for more details. 15 | # 16 | # You should have received a copy of the GNU General Public License 17 | # along with Tkinter3D. If not, see . 18 | # 19 | ''' 20 | Classes and functions for doing 3D math with quaternions. 21 | ''' 22 | from math import sin, cos, pi, sqrt, acos, atan2, asin 23 | from operator import add, sub, mul #, div 24 | from operator import truediv as div 25 | 26 | 27 | tolerance = 0.00001 # A value "close enough" to zero. 28 | 29 | #: Tuple of scalar numeric types: int, float, and long. 30 | #: (If you import :mod:`math3d` and change this before importing other 31 | #: modules in this package it will affect their type-checking behavior.) 32 | scalar_types = int, float #, long 33 | 34 | 35 | radians = 180 / pi 36 | 37 | 38 | def r2d(n): 39 | return n * radians 40 | 41 | 42 | class Quaternion: 43 | 44 | def __init__(self, n=0.0, x=0.0, y=0.0, z=0.0, euler=False): 45 | self.n = n 46 | 47 | if isinstance(x, Vector): 48 | assert not euler #if euler, x,y,z should be angles 49 | self.v = x 50 | 51 | elif euler: 52 | #create Q from Euler angles 53 | x, y, z = ( 54 | n / radians / 2.0 55 | for n in (x, y, z) 56 | ) 57 | 58 | Q = ( 59 | Quaternion(cos(x), sin(x)) 60 | * 61 | Quaternion(cos(y), 0.0, sin(y)) 62 | * 63 | Quaternion(cos(z), 0.0, 0.0, sin(z)) 64 | ) 65 | self.n = Q.n 66 | self.v = Q.v 67 | 68 | else: 69 | self.v = Vector(x, y, z) 70 | 71 | def __repr__(self): 72 | return "" % (self.n, self.v.__repr__()) 73 | 74 | def magnitude(self): 75 | v = self.v 76 | return sqrt(sum(( 77 | self.n * self.n, 78 | v.x * v.x, 79 | v.y * v.y, 80 | v.z * v.z 81 | ))) 82 | 83 | def getVector(self): 84 | return Vector(self.v.x, self.v.y, self.v.z) 85 | 86 | def getScalar(self): 87 | return self.n 88 | 89 | def __add__(self, p): 90 | if not isinstance(p, Quaternion): 91 | raise TypeError 92 | return Quaternion(self.n + p.n, self.v + p.v) 93 | 94 | def __sub__(self, p): 95 | if not isinstance(p, Quaternion): 96 | raise TypeError 97 | return Quaternion(self.n-p.n, self.v-p.v) 98 | 99 | def __mul__(self, p): 100 | if isinstance(p, scalar_types): 101 | return Quaternion(self.n * p, self.v * p) 102 | 103 | elif isinstance(p, Quaternion): 104 | return Quaternion( 105 | self.n * p.n - self.v * p.v, # the real part "n" 106 | ( 107 | p.v * self.n 108 | + self.v * p.n 109 | + self.v ^ p.v 110 | ) 111 | ) 112 | 113 | elif isinstance(p, Vector): 114 | return self * Quaternion(0.0, p) 115 | 116 | else: 117 | #raise TypeError, p 118 | raise TypeError 119 | 120 | def __div__(self, p): 121 | if not isinstance(p, scalar_types): 122 | raise TypeError 123 | return Quaternion(self.n / p, self.v / p) 124 | 125 | def __invert__(self): 126 | """Return the conjugate itself.""" 127 | return Quaternion(self.n, ~self.v) 128 | 129 | def getAngle(self): 130 | """Angle of rotation about axis.""" 131 | return 2 * acos(self.n) 132 | 133 | def getAxis(self): 134 | m = self.v.magnitude() 135 | if m <= tolerance: 136 | return Vector() 137 | else: 138 | return self.v / m 139 | 140 | def Rotate(q, p): 141 | if not isinstance(p, Quaternion): 142 | raise TypeError 143 | return q * p * (~q) 144 | 145 | def vectorRotate(q, v): 146 | if not isinstance(v, Vector): 147 | raise TypeError 148 | t = q * v * (~q) 149 | return t.getVector() 150 | 151 | def getEulerAngles(q): 152 | q00 = q.n * q.n 153 | q11 = q.v.x * q.v.x 154 | q22 = q.v.y * q.v.y 155 | q33 = q.v.z * q.v.z 156 | 157 | r11 = q00 + q11 - q22 - q33 158 | r21 = 2 * (q.v.x * q.v.y + q.n * q.v.z) 159 | r31 = 2 * (q.v.x * q.v.z + q.n * q.v.y) 160 | r32 = 2 * (q.v.y * q.v.z + q.n * q.v.x) 161 | r33 = q00 - q11 - q22 + q33 162 | 163 | tmp = abs(r31) 164 | if tmp > 0.999999: 165 | r12 = 2 * (q.v.x * q.v.y - q.n * q.v.z) 166 | r13 = 2 * (q.v.x * q.v.z + q.n * q.v.y) 167 | 168 | return Vector( 169 | 0.0, 170 | r2d(-(pi / 2) * (r31 / tmp)), 171 | r2d(atan2(-r12, -r31*r13)) 172 | ) 173 | return Vector( 174 | r2d(atan2(r32, r33)), 175 | r2d(asin(-r31)), 176 | r2d(atan2(r21, r11)) 177 | ) 178 | 179 | 180 | class Vector: 181 | """ 182 | This defines a vector of three coordinates. 183 | """ 184 | 185 | def __init__(self, x=0.0, y=0.0, z=0.0): 186 | self.x = x 187 | self.y = y 188 | self.z = z 189 | 190 | def __repr__(self): 191 | return "" % (self.x, self.y, self.z) 192 | 193 | def magnitude(self): 194 | ''' 195 | Return the scalar magnitude (length from origin) of this Vector. 196 | 197 | :rtype: :obj:`float` 198 | 199 | ''' 200 | return sqrt( 201 | self.x * self.x + 202 | self.y * self.y + 203 | self.z * self.z 204 | ) 205 | 206 | def normalize(self): 207 | ''' 208 | Return a Vector of magnitude 1 pointing in the same direction as 209 | this Vector. 210 | 211 | :rtype: :class:`Vector` 212 | 213 | ''' 214 | m = self.magnitude() 215 | if m < tolerance: 216 | m = 1 217 | xyz = [self.x / m, self.y / m, self.z / m] 218 | for i in (0, 1, 2): 219 | if abs(xyz[i]) < tolerance: 220 | xyz[i] = 0.0 221 | return Vector(*xyz) 222 | 223 | def reverse(self): 224 | ''' 225 | Return a Vector pointing in the opposite direction from this one. 226 | 227 | :rtype: :class:`Vector` 228 | 229 | ''' 230 | return Vector(-self.x, -self.y, -self.z) 231 | 232 | def __add__(self, r_v): 233 | if not isinstance(r_v, Vector): 234 | raise TypeError 235 | return Vector(self.x + r_v.x, self.y + r_v.y, self.z + r_v.z) 236 | 237 | def __sub__(self, r_v): 238 | if not isinstance(r_v, Vector): 239 | raise TypeError 240 | return Vector(self.x - r_v.x, self.y - r_v.y, self.z - r_v.z) 241 | 242 | def __mul__(self, r_n): 243 | if isinstance(r_n, Vector): 244 | #Dot Product 245 | return sum(( 246 | self.x * r_n.x, 247 | self.y * r_n.y, 248 | self.z * r_n.z 249 | )) 250 | 251 | elif isinstance(r_n, Matrix): 252 | #Matrix multiplication 253 | return r_n.__mul__(self) 254 | 255 | elif isinstance(r_n, scalar_types): 256 | #Scalar multiplication 257 | return Vector(self.x * r_n, self.y * r_n, self.z * r_n) 258 | 259 | else: 260 | #raise TypeError, r_n 261 | raise TypeError 262 | 263 | def __div__(self, r_n): 264 | if not isinstance(r_n, scalar_types): 265 | raise TypeError 266 | return Vector(self.x / r_n, self.y / r_n, self.z / r_n) 267 | 268 | def __neg__(self): 269 | return self.reverse() 270 | 271 | def __invert__(self): 272 | return self.reverse() 273 | 274 | def __xor__(self, other): 275 | """Note: NOT eXclusive-OR, Vector Cross Product.""" 276 | if not isinstance(other, Vector): 277 | raise TypeError 278 | return Vector( 279 | self.y * other.z - self.z * other.y, 280 | -self.x * other.z + self.z * other.x, 281 | self.x * other.y - self.y * other.x 282 | ) 283 | 284 | def triplescalar(self, v, w): 285 | if not (isinstance(v, Vector) 286 | and isinstance(w, Vector)): 287 | raise TypeError 288 | res = self * (v ^ w) 289 | if abs(res) < tolerance: 290 | res = 0.0 291 | return res 292 | 293 | 294 | class Matrix: 295 | 296 | make_local_variables = """\ 297 | e11=self.e11; e12=self.e12; e13=self.e13 298 | e21=self.e21; e22=self.e22; e23=self.e23 299 | e31=self.e31; e32=self.e32; e33=self.e33 300 | """ 301 | 302 | def __init__(self, 303 | e11=0.0, e12=0.0, e13=0.0, 304 | e21=0.0, e22=0.0, e23=0.0, 305 | e31=0.0, e32=0.0, e33=0.0 306 | ): 307 | self.e11 = e11 308 | self.e12 = e12 309 | self.e13 = e13 310 | self.e21 = e21 311 | self.e22 = e22 312 | self.e23 = e23 313 | self.e31 = e31 314 | self.e32 = e32 315 | self.e33 = e33 316 | 317 | def __repr__(self): 318 | exec(self.make_local_variables) 319 | return "" % ( 320 | e11, e12, e13, 321 | e21, e22, e23, 322 | e31, e32, e33 323 | ) 324 | 325 | def determinant(self): 326 | exec(self.make_local_variables) 327 | return e11*e22*e33 - \ 328 | e11*e32*e23 + \ 329 | e21*e32*e13 - \ 330 | e21*e12*e33 + \ 331 | e31*e12*e23 - \ 332 | e31*e22*e13 333 | 334 | def transpose(self): 335 | exec(self.make_local_variables) 336 | return Matrix( 337 | e11, e21, e31, 338 | e12, e22, e32, 339 | e13, e23, e33 340 | ) 341 | 342 | def __invert__(self): 343 | """~M""" 344 | exec(self.make_local_variables) 345 | d = self.determinant() 346 | if d == 0.0: 347 | d = 1.0 348 | return Matrix(*[ 349 | n / d 350 | for n in ( 351 | e22*e33 - e23*e32, -(e12*e33 - e13*e32), e12*e23 - e13*e22, 352 | -(e21*e33 - e23*e31), e11*e33 - e13*e31, -(e11*e23 - e13*e21), 353 | e21*e32 - e22*e31, -(e11*e32 - e12*e31), e11*e22 - e12*e21 354 | ) 355 | ]) 356 | # N.B. I had to add the '*[]' notation in the above call to 357 | # Matrix() because of a weird interaction with the exec: 358 | # 359 | # $ python math3d.py 360 | # File "math3d.py", line 298 361 | # exec self.make_local_variables 362 | # SyntaxError: unqualified exec is not allowed in function 363 | # '__invert__' it contains a nested function with free variables 364 | # 365 | 366 | def __op(n, m, op): #Note the arg traditionally called 'self' is here called 'n' 367 | """This function applies the op 'op' to each element pair of two matricies.""" 368 | ne = [ 369 | n.e11, n.e12, n.e13, 370 | n.e21, n.e22, n.e23, 371 | n.e31, n.e32, n.e33 372 | ] 373 | me = [ 374 | m.e11, m.e12, m.e13, 375 | m.e21, m.e22, m.e23, 376 | m.e31, m.e32, m.e33 377 | ] 378 | return Matrix(*map(op, ne, me)) 379 | 380 | def __add__(self, r_v): 381 | if isinstance(r_v, scalar_types): 382 | # For scalar addition we convert the scalar value into a 383 | # matrix containing the scalar value in every element and 384 | # then add it, below. 385 | r_v = Matrix(*((r_v,) * 9)) 386 | 387 | elif not isinstance(r_v, Matrix): 388 | #raise TypeError, r_v 389 | raise TypeError 390 | 391 | return self.__op(r_v, add) 392 | 393 | def __sub__(self, r_v): 394 | if isinstance(r_v, scalar_types): 395 | r_v = Matrix(*((r_v,) * 9)) 396 | 397 | elif not isinstance(r_v, Matrix): 398 | #raise TypeError, r_v 399 | raise TypeError 400 | 401 | return self.__op(r_v, sub) 402 | 403 | def __mul__(self, r_n): 404 | 405 | if isinstance(r_n, Matrix): 406 | 407 | exec(self.make_local_variables) 408 | 409 | me11=r_n.e11; me12=r_n.e12; me13=r_n.e13 410 | me21=r_n.e21; me22=r_n.e22; me23=r_n.e23 411 | me31=r_n.e31; me32=r_n.e32; me33=r_n.e33 412 | 413 | return Matrix( 414 | self.e11*me11 + self.e12*me21 + self.e13*me31, 415 | self.e11*me12 + self.e12*me22 + self.e13*me32, 416 | self.e11*me13 + self.e12*me23 + self.e13*me33, 417 | 418 | self.e21*me11 + self.e22*me21 + self.e23*me31, 419 | self.e21*me12 + self.e22*me22 + self.e23*me32, 420 | self.e21*me13 + self.e22*me23 + self.e23*me33, 421 | 422 | self.e31*me11 + self.e32*me21 + self.e33*me31, 423 | self.e31*me12 + self.e32*me22 + self.e33*me32, 424 | self.e31*me13 + self.e32*me23 + self.e33*me33, 425 | ) 426 | 427 | if isinstance(r_n, Vector): 428 | 429 | exec(self.make_local_variables) 430 | 431 | return Vector( 432 | self.e11*r_n.x + self.e12*r_n.y + self.e13*r_n.z, 433 | self.e21*r_n.x + self.e22*r_n.y + self.e23*r_n.z, 434 | self.e31*r_n.x + self.e32*r_n.y + self.e33*r_n.z 435 | ) 436 | 437 | if isinstance(r_n, scalar_types): 438 | tmp = Matrix(*((r_n,) * 9)) 439 | return self.__op(tmp, mul) 440 | 441 | #raise TypeError, r_n 442 | raise TypeError 443 | 444 | def __div__(self, r_n): 445 | if not isinstance(r_n, scalar_types): 446 | raise TypeError 447 | return self.__op(Matrix(*((r_n,) * 9)), div) 448 | 449 | 450 | def planeNormalAndDistance(v0, v1, v2): 451 | pN = (v2 - v0) ^ (v1 - v0) 452 | pN = pN.normalize() 453 | d = v0 * pN 454 | return pN, d 455 | 456 | 457 | def Frustum2Planes(f): 458 | v0, v1, v2, v3, v4, v5, v6, v7 = f 459 | lpN, ld = planeNormalAndDistance(v0, v4, v3) 460 | rpN, rd = planeNormalAndDistance(v6, v2, v5) 461 | tpN, td = planeNormalAndDistance(v3, v7, v1) 462 | bpN, bd = planeNormalAndDistance(v2, v6, v0) 463 | return (lpN, ld), (rpN, rd), (tpN, td), (bpN, bd) 464 | 465 | 466 | def distanceVector2Plane(pN, pd, v): 467 | return pN * v - pd 468 | 469 | 470 | def distanceVector2PlanePlus(pN, pd, v): 471 | return pN.x*v.x + pN.y*v.y + pN.z*v.z - pd 472 | 473 | 474 | 475 | def rotx(a): 476 | a = a / radians 477 | return Matrix( 478 | 1, 0, 0, 479 | 0, cos(a), -sin(a), 480 | 0, sin(a), cos(a) 481 | ) 482 | 483 | 484 | def roty(a): 485 | a = a / radians 486 | return Matrix( 487 | cos(a), 0, sin(a), 488 | 0, 1, 0, 489 | -sin(a), 0, cos(a) 490 | ) 491 | 492 | 493 | def rotz(a): 494 | """Clockwise as facing z+ """ 495 | a = a / radians 496 | return Matrix( 497 | cos(a), -sin(a), 0, 498 | sin(a), cos(a), 0, 499 | 0, 0, 1 500 | ) 501 | -------------------------------------------------------------------------------- /neat_demo.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # 3 | # Copyright 2011, 2012, 2013, 2014 Simon Forman 4 | # 5 | # This file is part of Tkinter3D. 6 | # 7 | # Tkinter3D is free software: you can redistribute it and/or modify 8 | # it under the terms of the GNU General Public License as published by 9 | # the Free Software Foundation, either version 3 of the License, or 10 | # (at your option) any later version. 11 | # 12 | # Tkinter3D is distributed in the hope that it will be useful, 13 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | # GNU General Public License for more details. 16 | # 17 | # You should have received a copy of the GNU General Public License 18 | # along with Tkinter3D. If not, see . 19 | # 20 | from tkinter import Tk 21 | from canvas3d import Canvas3D, Frame3D, roty 22 | from scene import Thing3D as dot 23 | 24 | 25 | root = Tk() 26 | root.title("Rotating Cube Demo") 27 | c = Canvas3D(root) 28 | c.pack(expand=1, fill='both') 29 | 30 | 31 | # Zoom out a little. 32 | c.frame.T.z += -300.0 33 | 34 | 35 | # Create a dot at world origin (0, 0, 0). 36 | origin = dot(c, width=4) 37 | c.frame.things.append(origin) 38 | 39 | 40 | # Make a frame for some objects to be in. 41 | cube_frame = Frame3D() 42 | c.frame.subframes.append(cube_frame) 43 | 44 | 45 | # Add a Z component to the cube frame's translation to offset the cube 46 | # from the world frame. 47 | cube_frame.T.z += 300.0 48 | 49 | 50 | # Make a cube. 51 | F = -100.0, 100.0 52 | for x, y, z in ((x, y, z) for x in F for y in F for z in F): 53 | cube_frame.things.append(dot(c, x, y, z, width=6)) 54 | 55 | 56 | # Apply a rotation repeatedly to our cube. 57 | rotation = roty(360/30/3) # 4 degrees. 58 | def delta(): 59 | cube_frame.RM *= rotation 60 | c.after(60, delta) # Retrigger every sixty milliseconds. 61 | 62 | 63 | # Start everything running. 64 | delta() 65 | c.start_updating() 66 | root.mainloop() 67 | -------------------------------------------------------------------------------- /scene.py: -------------------------------------------------------------------------------- 1 | # 2 | # Copyright 2011, 2012, 2013, 2014 Simon Forman 3 | # 4 | # This file is part of Tkinter3D. 5 | # 6 | # Tkinter3D is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # 11 | # Tkinter3D is distributed in the hope that it will be useful, 12 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 13 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 | # GNU General Public License for more details. 15 | # 16 | # You should have received a copy of the GNU General Public License 17 | # along with Tkinter3D. If not, see . 18 | # 19 | 20 | from math3d import ( 21 | scalar_types, 22 | Vector, 23 | Matrix, 24 | rotx, 25 | roty, 26 | rotz, 27 | ) 28 | 29 | 30 | class Frame3D: 31 | ''' 32 | A frame of reference for applying a scale, translation, and rotation 33 | to a collection of :class:`Thing3D` objects. It can also have 34 | descendant :class:`Frame3D` objects that contain their own 35 | :class:`Thing3D` objects. 36 | 37 | :param scale: A scaling factor. 38 | :type scale: One of :data:`math3d.scalar_types` 39 | 40 | :param translation: Specifies XYZ translation. 41 | :type translation: :class:`math3d.Vector` or any iterable of any 42 | three :data:`math3d.scalar_types` 43 | 44 | :param rotation: Specifies a rotation around each of the X, Y, and Z 45 | axises. If given as discrete values (i.e. not a 46 | :class:`math3d.Matrix`) they are interpreted as degrees. 47 | :type rotation: :class:`math3d.Matrix` or any iterable of any 48 | three :data:`math3d.scalar_types` 49 | 50 | :raises: :exc:`TypeError` if the constraints on parameters are not 51 | met. 52 | 53 | Each of the above three parameters becomes an instance attribute of 54 | the resulting :class:`Frame3D` object that you can manipulate at 55 | runtime to affect subsequent calls to :meth:`yieldTransformed`. 56 | 57 | 58 | .. attribute:: s 59 | 60 | (Instance attribute.) Scale factor applied by 61 | :meth:`yieldTransformed`. 62 | 63 | .. attribute:: T 64 | 65 | (Instance attribute.) :class:`math3d.Vector` Translation applied 66 | by :meth:`yieldTransformed`. 67 | 68 | .. attribute:: RM 69 | 70 | (Instance attribute.) :class:`math3d.Matrix` Rotation applied by 71 | :meth:`yieldTransformed`. 72 | 73 | .. attribute:: things 74 | 75 | (Instance attribute.) A list of :class:`Thing3D` objects. Append 76 | :class:`Thing3D` objects to this list to have them yielded by 77 | :meth:`yieldTransformed`. 78 | 79 | .. attribute:: subframes 80 | 81 | (Instance attribute.) A list of :class:`Frame3D` objects. Append 82 | :class:`Frame3D` objects to this list to have their 83 | :class:`Thing3D` objects yielded by :meth:`yieldTransformed`. 84 | 85 | ''' 86 | 87 | def __init__( 88 | self, 89 | scale=1.0, 90 | translation=None, 91 | rotation=None, 92 | ): 93 | 94 | self.things = [] 95 | self.subframes = [] 96 | 97 | if not isinstance(scale, scalar_types): 98 | #raise TypeError, scale 99 | raise TypeError 100 | self.s = scale 101 | 102 | # Translation. 103 | if isinstance(translation, Vector): 104 | self.T = translation 105 | 106 | elif translation is not None: 107 | 108 | translation = tuple(translation) 109 | 110 | if not ( 111 | len(translation) == 3 112 | and all(isinstance(t, scalar_types) for t in translation) 113 | ): 114 | #raise TypeError, translation 115 | raise TypeError 116 | 117 | self.T = Vector(*translation) 118 | 119 | else: 120 | self.T = Vector() 121 | 122 | # Rotation. 123 | if isinstance(rotation, Matrix): 124 | self.RM = rotation 125 | 126 | elif rotation is not None: 127 | 128 | rotation = tuple(rotation) 129 | 130 | if not ( 131 | len(rotation) == 3 132 | and all(isinstance(a, scalar_types) for a in rotation) 133 | ): 134 | #raise TypeError, rotation 135 | raise TypeError 136 | 137 | ax, ay, az = rotation 138 | self.RM = rotx(ax) * roty(ay) * rotz(az) 139 | 140 | else: 141 | self.RM = rotx(0) * roty(0) * rotz(0) 142 | 143 | def transform(self, vector): 144 | ''' 145 | Return a Vector that is the result of appling the scale, 146 | translation, and rotation defined by this :class:`Frame3D` to the 147 | given input Vector. 148 | 149 | :param vector: A Vector representing a 3D point. 150 | :type vector: :class:`math3d.Vector` 151 | :rtype: :class:`math3d.Vector` 152 | 153 | ''' 154 | if self.s != 1: 155 | vector = vector * self.s 156 | return (vector - self.T) * self.RM 157 | 158 | def yieldTransformed(self): 159 | ''' 160 | Yield each :class:`Thing3D` in this :class:`Frame3D` and its 161 | descendant :class:`Frame3D` objects, modified by its scale, 162 | translation, and rotation. 163 | This is called recursively on descendant :class:`Frame3D` objects. 164 | 165 | :rtype: generator of two-tuples: 166 | (:class:`Thing3D`, transformed :class:`math3d.Vector`) 167 | 168 | ''' 169 | for subframe in self.subframes: 170 | for thing, vector in subframe.yieldTransformed(): 171 | yield thing, self.transform(vector) 172 | for thing in self.things: 173 | yield thing, self.transform(thing.vector) 174 | 175 | 176 | class Thing3D: 177 | ''' 178 | A thing that has a location in three-space and knows how to render 179 | itself on a :class:`canvas3d.Canvas3D`. The default rendering is a 180 | circle. 181 | 182 | Once a :class:`Thing3D` is created it must be appended to a 183 | :attr:`Frame3D.things` list and that :class:`Frame3D` 184 | must be the frame of a :class:`canvas3d.Canvas3D` or one of its 185 | descendant frames in order for the :class:`Thing3D` to be rendered. 186 | 187 | :param canvas: A Canvas3D object to render on. The :class:`Thing3D` 188 | must be appended to its :class:`Frame3D` or one of that frame's 189 | descendant frames in order to be rendered. 190 | :type canvas: :class:`canvas3d.Canvas3D` 191 | 192 | :param x: X coordinate. 193 | :type x: One of :data:`math3d.scalar_types` 194 | 195 | :param y: Y coordinate. 196 | :type y: One of :data:`math3d.scalar_types` 197 | 198 | :param z: Z coordinate. 199 | :type z: One of :data:`math3d.scalar_types` 200 | 201 | :param settings: Any number of addtional keyword arguments can be 202 | passed in to modify the Tkinter Canvas item used to render the 203 | :class:`Thing3D`. (I.e. ``fill`` can be a color name.) One special 204 | keyword argument ``width`` (:obj:`int`) is used to set the width 205 | of the rendered circle, it defaults to 3. See the Tkinter Canvas 206 | docs for more information. 207 | 208 | ''' 209 | 210 | def __init__(self, canvas, x=0.0, y=0.0, z=0.0, **settings): 211 | 212 | self.vector = Vector(x, y, z) 213 | 214 | self.canvas = canvas 215 | 216 | # Width in pixels of canvas dot. 217 | self._width = settings.pop('width', None) or 3 218 | 219 | self.settings = settings 220 | self.settings.setdefault('fill', 'green') 221 | 222 | # Canvas item id for our vector/dot. 223 | self.item = None 224 | 225 | def hide(self): 226 | ''' 227 | Hide this :class:`Thing3D`. 228 | 229 | Normally only called by its :class:`canvas3d.Canvas3D` during 230 | rendering when it has moved out of the viewable space. 231 | ''' 232 | if self.item: 233 | self.canvas.delete(self.item) 234 | self.item = None 235 | 236 | def render(self, x, y, z): 237 | ''' 238 | Draw this :class:`Thing3D` on its :class:`canvas3d.Canvas3D`. 239 | 240 | Normally only called by its :class:`canvas3d.Canvas3D` during 241 | rendering to update its postion. 242 | 243 | :param x: X coordinate in Canvas screen coordinates. 244 | :type x: :obj:`int` 245 | 246 | :param y: Y coordinate in Canvas screen coordinates. 247 | :type y: :obj:`int` 248 | 249 | :param z: Z depth, **not used**. 250 | 251 | ''' 252 | 253 | width = self._width 254 | half = width / 2 255 | 256 | top, left = x - half, y - half 257 | bottom, right = top + width, left + width 258 | 259 | # Move our item if we have one. 260 | if self.item: 261 | self.canvas.coords(self.item, top, left, bottom, right) 262 | 263 | # Make an oval item and remember its id. 264 | else: 265 | self.item = self.canvas.create_oval( 266 | top, 267 | left, 268 | bottom, 269 | right, 270 | **self.settings 271 | ) 272 | --------------------------------------------------------------------------------