Fundamental geometric transformation, Mechanical Engineering

Fundamental geometric transformation:

The fundamental geometric transformation is Rotation, Translations and Scaling. Other transformations involve reflection and shearing. Translation moves object in a straight line path from one position to another while rotation moves the object in a circular path around a rotation point. In scaling, dimensions of an object changes relating to a specified fixed point. Reflections are transformation that rotates an object by 180o around reflection axis to generate a mirror image of the object w.r.t. that axis. Shearing transformation distorts the object shape by shifting X or Y coordinating values. Transformation matrices may be calculated by concatenation of different matrices while we apply number of transformation to the object at a time. In the second half, different kinds of planar projections are discussed. In orthographic projections, projectors are parallel to each other and also perpendicular to view plane. Orthographic projections are further categorized as multi view or axonometric. Multi view projection displays single face of a three-dimensional object and the view plane normal is generally parallel to one of the major axis while in case of axonometric projection is not parallel to any of the major axis. Axonometric projections may be classified as diametric, trimetric or isometric. There is second category of parallel projection that means oblique projections where the angle between the projectors and view plane is no longer normal. At last, one- point, two-point and three-point perspective projections are also explained.

Posted Date: 1/24/2013 4:59:03 AM | Location : United States

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