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<title>Generative Modelling Language</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Generative Modelling Language</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable">This article is about computer graphics and generative computer programming. For generative models of <a href="Markov_decision_processes" class="mw-redirect" title="Markov decision processes">Markov decision processes</a>, see <a href="Markov_decision_process#Simulator_models" title="Markov decision process">Markov decision process § Simulator models</a>. For generative models in the context of statistical classification, see <a href="Generative_model" title="Generative model">Generative model</a>. For Generative Artificial Intelligence (Generative A.I.) models/systems, see <a href="Generative_artificial_intelligence" title="Generative artificial intelligence">Generative artificial intelligence</a>.</div><p><b>Generative Modelling Language</b> (GML) in <a href="Computer_graphics" title="Computer graphics">computer graphics</a> and <a href="Generative_computer_programming" class="mw-redirect" title="Generative computer programming">generative computer programming</a> is a very simple programming language for the concise description of complex 3D shapes. It follows the "Generative Modelling" paradigm, where complex datasets are represented by "lists of operations" rather than by lists of objects, which is for instance the case in a <a href="Relational_database" title="Relational database">relational database</a>.

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<div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2></div>

<p>Usual <a href="3D_file_formats" class="mw-redirect" title="3D file formats">3D file formats</a> describe a <a href="Virtual_world" title="Virtual world">virtual world</a> in terms of <a href="Geometric_primitive" title="Geometric primitive">geometric primitives</a>. These may be cubes and spheres in a <a href="Constructive_solid_geometry" title="Constructive solid geometry">CSG</a> tree, <a href="NURBS" class="mw-redirect" title="NURBS">NURBS</a> patches, a set of <a href="Implicit_function" title="Implicit function">implicit functions</a>, a <a href="Triangle_mesh" title="Triangle mesh">triangle mesh</a>, or just a <a href="Point_cloud" title="Point cloud">cloud of points</a>. The term "generative 3D modelling" describes a different paradigm for describing shape. The main idea is to replace 3D objects by object-generating operations: A shape is described by a sequence of processing steps, rather than the triangles which are the result of applying these operations. Shape design becomes rule design. The approach can be generally applied to any shape representation that provides a basic set of generating functions, called in this context 'elementary shape operators'. Its effectiveness has been demonstrated, e.g., in the field of procedural <a href="Mesh_generation" title="Mesh generation">mesh generation</a>, with <a href="Euler_operator_(digital_geometry)" title="Euler operator (digital geometry)">Euler operators</a> as complete and closed set of invertible shape generating functions for meshes, operating on the half-edge level.

</p><p>Generative modelling gains efficiency through the possibility of creating high-level shape operators from low-level shape operators. Any sequence of processing steps can be grouped together to create a new <i>combined operator</i>. It may use elementary operators as well as other combined operators. Concrete values can easily be replaced by parameters, which makes it possible to separate data from operations: The same processing sequence can be applied to different input data sets. The same data can be used to produce different shapes by applying different combined operators from, e.g., a library of domain-dependent modelling operators. This makes it possible to create very complex objects from only a few high-level input parameters, such as for instance a style library.

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<div class="mw-heading mw-heading2"><h2 id="The_Generative_Modelling_Language">The Generative Modelling Language</h2></div>

<p>The GML is a concrete implementation of the generative approach. It is a stack-based, <a href="Interpreted_programming_language" class="mw-redirect" title="Interpreted programming language">interpreted programming language</a>, very similar to Adobe's <a href="PostScript" title="PostScript">PostScript</a>, but without any of the 2D layout operators. It provides instead a number of operators for creating 3D models (<a href="Polygon" title="Polygon">polygons</a>, <a href="B-rep" class="mw-redirect" title="B-rep">b-reps</a>, <a href="Subdivision_surface" title="Subdivision surface">subdivision surfaces</a>). As a "shape programming language," it is a true generalization of "flat" 3D file formats like <a href="Wavefront_.obj_file" title="Wavefront .obj file">OBJ</a>, <a href="DXF" class="mw-redirect" title="DXF">DXF</a>, or <a href="VRML" title="VRML">VRML</a> that contain just lists of geometric primitives.

</p><p>Together with its <a href="OpenGL" title="OpenGL">OpenGL</a>-based <a href="Runtime_engine" class="mw-redirect" title="Runtime engine">runtime engine</a> the GML can also be seen as a viewer with an integrated modeller, to overcome the usual separation of <a href="3D_modeling" title="3D modeling">3D modelling</a> from <a href="Real-time_computer_graphics" title="Real-time computer graphics">interactive visualization</a>. Both are interwoven instead. GML permits a concise representation of parameterized 3D objects which can be evaluated on-the-fly at runtime, rendered with <a href="Level_of_detail_(computer_graphics)" title="Level of detail (computer graphics)">adaptive level-of-detail</a>, and allows for the interactive manipulation of all parameters.

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<div class="mw-heading mw-heading2"><h2 id="GML_Example">GML Example</h2></div>

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<td>(0,0,-2) (1,1,0) 2 quad

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<td>/cyan setcurrentmaterial

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<td>5 poly2doubleface

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<td>(0,1,1) extrude

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<td>(0,0,1) (1,0,1) normalize

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<td>0 project_ringplane

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<td>(2,0,0) (0,1,-1) 2 quad

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<td>/yellow setcurrentmaterial

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<td>5 poly2doubleface

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<td>0 bridgerings

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<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

</p><p>With procedural models, the model complexity is no longer directly (i.e., linearly) related with the file size. The <i>Procedural Cathedral</i>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> a basic model of the <a href="Cologne_Cathedral" title="Cologne Cathedral">Cologne Cathedral</a>, contains 70 <a href="Tracery" title="Tracery">tracery</a> windows, and a single window in highest resolution contains about 7 million triangles. These are "unfolded" from only 126 KB of GML code (18 KB zipped).