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Fig.5: A second, horizontal plane of projection is added, perpendicular to the first. Fig.6: Projectors emanate parallel from all points of the object perpendicular to the second plane of projection. Fig.7: An image is created thereby. Fig.8: The third plane of projection is added, perpendicular to the previous two.
Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. [1]
Note that with the cube (see image) the perimeter of the resulting 2D drawing is a perfect regular hexagon: all the black lines have equal length and all the cube's faces are the same area. Isometric graph paper can be placed under a normal piece of drawing paper to help achieve the effect without calculation.
Orthographic projection (also orthogonal projection and analemma) [a] is a means of representing three-dimensional objects in two dimensions.Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, [2] resulting in every plane of the scene appearing in affine transformation on the viewing surface.
Live Geometry is a free CodePlex project that lets you create interactive ruler and compass constructions and experiment with them. It is written in Silverlight 4 and C# 4.0 (Visual Studio 2010). The core engine is a flexible and extensible framework that allows easy addition of new figure types and features.
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For example, when α is the ground plane and β is the horizon plane, then the vanishing line of α is the horizon line β ∩ π. To put it simply, the vanishing line of some plane, say α , is obtained by the intersection of the image plane with another plane, say β , parallel to the plane of interest ( α ), passing through the camera center.
SolveSpace is a free and open-source 2D/3D constraint-based parametric computer-aided design (CAD) software that supports basic 2D and 3D constructive solid geometry modeling. It is a constraint-based parametric modeler with simple mechanical simulation capabilities. Version 2.1 and onward runs on Windows, Linux and macOS.