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‎01-preface.rst

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This book is open-access (i.e. it's free to read at `this address
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<http://www.labri.fr/perso/nrougier/python+opengl>`_) because I believe
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knowledge should be free. However, if you think the book is worth a few
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dollars, you can `Buy the book`_. This money will help me to travel to Python
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conferences and to write other books as well. If you don't have money, it's
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fine. Just enjoy the book and spread the word about it. The teaser image above
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comes from the `artwork section
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dollars, you can give me a few euros (`5€
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<https://www.paypal.me/NicolasPRougier/5>`_ or `10€
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<https://www.paypal.me/NicolasPRougier/10>`_). This money will help me to
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travel to Python conferences and to write other books as well. If you don't
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have money, it's fine. Just enjoy the book and spread the word about it. The
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teaser image above comes from the `artwork section
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<http://www.labri.fr/perso/nrougier/artwork/index.html>`_ of my website. It has
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been made some years ago using the `Povray <http://www.povray.org>`_
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(Persistence of Vision) raytracer. I like it very much because it is a kind of
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Buy the book
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-------------------------------------------------------------------------------
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As you may have realized by now, the book is free for you to read
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online. However, some people prefer to have a PDF version or even a dead-tree
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version. For this to happen, I need to design a latex template for producing a
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nice PDF. That's a lot of work and I don't really have time since I'm also (and
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mainly) a `researcher
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<http://www.labri.fr/perso/nrougier/research/index.html>`_ with several
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students to supervise, researches to do, articles and grants to write, talks to
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prepare, etc.
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Consequently, if you really want to have a PDF version, you'll have to
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explicitly express your interest by contributing a small amount of
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money. Then,
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* if the total reach **5,000 euros**, I'll produce the PDF
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* if the total reach **10,000 euros**, I'll have the book printed and sold (20 euros).
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However, be warned that you won't get refund if the first goal is not
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reached. In such case, consider your payment as a donation to the online
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version. If you find this unfair, remember you have the choice to give or not
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and the online version is free and open source...
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.. image:: images/chapter-01/crowdfunding.png
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:width: 100%
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.. class:: button
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* `5€ <https://www.paypal.me/NicolasPRougier/5>`_
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* `10€ <https://www.paypal.me/NicolasPRougier/10>`_
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* `25€ <https://www.paypal.me/NicolasPRougier/25>`_
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* `50€ <https://www.paypal.me/NicolasPRougier/50>`_
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.. --- Links ------------------------------------------------------------------
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.. _Nicolas P. Rougier:
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http://www.labri.fr/perso/nrougier/

‎10-polygons.rst

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Rendering polygons
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===============================================================================
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figure above with the red lines.
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Convex polygons
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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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Convex polygons
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+++++++++++++++
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For convex polygons, we have to consider two cases:
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See `convex-polygon-fan.py <code/chapter-10/convex-polygon-fan.py>`_
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Concave polygons
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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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Concave polygons
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++++++++++++++++
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For concave polygons, we could consider the two aforementionned cases where
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points are either ordered and describe the contour of the polygon or points are
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.. _SVG Specification: https://www.w3.org/TR/SVG/painting.html
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Non-zero fill rule
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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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Non-zero fill rule
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++++++++++++++++++
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The non-zero fill rule implementation is easy because it corresponds to the
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default triangulation we've just seen above and no extra work is necessary.
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Odd-even fill rule
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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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Odd-even fill rule
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++++++++++++++++++
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In order to enforce the odd-even fill rule, we need to use a 2-pass
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rendering. The first pass will write to the stencil buffer according to the
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gl.glStencilOp(gl.GL_KEEP, gl.GL_KEEP, gl.GL_KEEP)
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Gradient and pattern
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-------------------------------------------------------------------------------
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Antialiasing
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-------------------------------------------------------------------------------
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Exercises
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-------------------------------------------------------------------------------
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Polygon gradients
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+++++++++++++++++
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.. figure:: images/chapter-10/radial-gradient.png
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:figwidth: 25%
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:figclass: right
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Figure
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Radial gradient.
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The SVG specification considers two kind of color gradients (i.e. smooth
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transition from one color to another), radial and linear. Using the vertices
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coordinates inside the shader, it is thus very easy to create those gradients.
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In order to do that, you need to compute (for every fragment) a scalar that
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indicate tells the amount of color 1 and color 2 respectively and try to render
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the image on the right.
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Solution: `radial-gradient.py <code/chapter-10/radial-gradient.py>`_
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Polygon Patterns
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++++++++++++++++
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.. figure:: images/chapter-10/pattern.png
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:figwidth: 25%
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:figclass: right
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Figure
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Patterns.
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We can also use any texture to pain the polygon. It's only a matter of
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assigning the right texture to polygon vertices. Try to render the image on the
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right using this `texture <images/chapter-10/wave.png>`_
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Solution: `pattern.py <code/chapter-10/pattern.py>`_
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Antialiasing
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++++++++++++
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As you have noticed, the polygon we've renderered so far are not antialised
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(because we've been using only raw triangles). While it might be possible to
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write a specific shader to take car of antiliasing on the border, it is far
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more easier to draw an antialiased polygon in two steps. First, we draw the
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interio of the polygon and then, we render a half-line on the contour. We need
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a half-line because we do not want the line to cover the already rendered
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polygon. There is no real difficulty and this is a good exercise. I will use
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the best proposed solution to be included here.
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‎11-meshes.rst

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Rendering a mesh
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===============================================================================
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.. contents:: .
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:local:
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:depth: 2
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:class: toc chapter-11
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Work in Progress.
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Implicit surfaces
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-----------------
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..
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.. contents:: .
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:local:
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:depth: 2
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:class: toc chapter-11
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Height fields
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-------------
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Mesh models
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-----------
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Ok, it is now time to go 3D! I'm pretty sure you're reading this book only for
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this. I won't explain everything since you'll find a lot of online resources
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dedicated to 3D rendering using OpenGL. Instead, I'll concentrate on common
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techniques found in scientific visualization. The teaser image is a Klein
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bottle rendered using glumpy. Sources are available from the
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`geometric-parametric.py
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<https://github.com/glumpy/glumpy/blob/master/examples/geometry-parametric.py>`_
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example.
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Parametric surfaces
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-------------------
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From Wikipedia:
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*A parametric surface is a surface in the Euclidean space ℝ³ which is
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defined by a parametric equation with two parameters f(u,v) : ℝ² →
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ℝ³. Parametric representation is a very general way to specify a surface,
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as well as implicit representation.*
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Surfaces such as `Boy's surface
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<https://en.wikipedia.org/wiki/Boy%27s_surface>`_, `Klein bottle
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<https://en.wikipedia.org/wiki/Klein_bottle>`_, `Möbius strip
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<https://en.wikipedia.org/wiki/Klein_bottle>`_ are all parametric surfaces that
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can be described using more or less simple equations. Let's consider the Boy's
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surface. Considering two parameters (u,v) in [0,π], the (x,y,z) surface writes (thanks `Mayavi <http://docs.enthought.com/mayavi/mayavi/auto/example_boy.html>`_):
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.. code:: python
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x = 2 / 3. * (cos(u) * cos(2 * v)
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+ sqrt(2) * sin(u) * cos(v)) * cos(u) / (sqrt(2) - sin(2 * u) * sin(3 * v))
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y = 2 / 3. * (cos(u) * sin(2 * v) -
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sqrt(2) * sin(u) * sin(v)) * cos(u) / (sqrt(2) - sin(2 * u) * sin(3 * v))
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z = -sqrt(2) * cos(u) * cos(u) / (sqrt(2) - sin(2 * u) * sin(3 * v))
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What is nice with such (u,v) parameterization is that we can easily triangulate
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the surface. We only have to iterate over u and v and compute the corresponding
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vertices:
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.. code:: python
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vtype = [('position', np.float32, 3)]
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vcount += 1
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ucount += 1
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n = vcount*ucount
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Un = np.repeat(np.linspace(0, 1, ucount, endpoint=True), vcount)
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U = umin+Un*(umax-umin) # normalization
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Vn = np.tile (np.linspace(0, 1, vcount, endpoint=True), ucount)
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V = vmin+Vn*(vmax-vmin) # normalization
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vertices = np.zeros(n, dtype=vtype)
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for i,(u,v) in enumerate(zip(U,V)):
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x,y,z = func(u,v)
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vertices["position"][i] = x,y,z
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Then (and because this a regular surface), we can easily build the
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corresponding indices:
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.. code:: python
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for i in range(ucount-1):
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for j in range(vcount-1):
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indices.append(i*(vcount) + j )
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indices.append(i*(vcount) + j+1 )
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indices.append(i*(vcount) + j+vcount+1)
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indices.append(i*(vcount) + j+vcount )
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indices.append(i*(vcount) + j+vcount+1)
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indices.append(i*(vcount) + j )
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indices = np.array(indices, dtype=itype)
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.. figure:: images/chapter-11/boy-tesselation.png
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:figwidth: 100%
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Figure
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Tesselated Boy's surface using 16, 32, 64 and 128 steps.
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See `boy-tesselation.py <code/chapter-11/boy-tesselation.py>`_
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.. figure:: movies/chapter-11/boy.mp4
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:figclass: right
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:loop:
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:autoplay:
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:controls:
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:figwidth: 35%
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Figure
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Colored Boy's surface using an approximated Viridis colormap by `Jérôme
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Liard <https://www.shadertoy.com/user/blackjero>`_.
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See `boy.py <code/chapter-11/boy.py>`_
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We can make the rendering a bit nicer using colors according to (u,v)
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coordinates. For this, we just need to provide the fragment shader with the
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(uv) coordinate and decide how to paint the surface acccording to u, v or both.
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Furthermore, instead of drawing the surface twices to display the grid lines,
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we can directly render them in the same shader.
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.. code:: glsl
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varying vec2 v_uv;
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void main()
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{
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float x = 1 - sin(v_uv.x);
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vec4 color = vec4(vec3(x), 1.0);
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vec4 black = vec4(vec3(0.0), 1.0);
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vec2 d = fract((v_uv/M_PI)*64.0);
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vec2 f = fwidth(d);
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vec2 a = smoothstep(0.99-f, 0.99+f, d);
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gl_FragColor = mix(color, black, max(a.x,a.y));
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}
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Height fields
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-------------
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Height fields are also a very common object in scientific visualization. It
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allows to visualize a function of the type z = f(x,y) over a specific domain.
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Mesh models
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-----------

‎12-text.rst

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Rendering text
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===============================================================================
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.. contents:: .
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:local:
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:depth: 2
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:class: toc chapter-12
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Work in Progress.
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Failsafe text
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-------------
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..
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.. contents:: .
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:local:
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:depth: 2
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:class: toc chapter-12
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2D text
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-------
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3D text
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-------
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Failsafe text
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-------------
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2D text
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-------
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3D text
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-------

‎13-framebuffer.rst

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Framebuffer
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===============================================================================
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.. contents:: .
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:local:
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:depth: 2
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:class: toc chapter-13
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Work in Progress.
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Post-processing
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---------------
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..
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.. contents:: .
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:local:
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:depth: 2
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:class: toc chapter-13
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General computation
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-------------------
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Post-processing
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---------------
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Color picking
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-------------
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General computation
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-------------------
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Color picking
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-------------

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