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Note for Computer Graphics - CG by Aarthi K

  • Computer Graphics - CG
  • Note
  • Sri Adi Chunchanagiri Women's College - SACWC
  • Information Technology Engineering
  • B.Tech
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  • Uploaded 11 months ago
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Application of Computer Graphics Computer Graphics has numerous applications, some of which are listed below − • • • • • • • • • • • • • • Computer graphics user interfaces (GUIs) − A graphic, mouse-oriented paradigm which allows the user to interact with a computer. Business presentation graphics − "A picture is worth a thousand words". Cartography − Drawing maps. Weather Maps − Real-time mapping, symbolic representations. Satellite Imaging − Geodesic images. Photo Enhancement − Sharpening blurred photos. Medical imaging − MRIs, CAT scans, etc. - Non-invasive internal examination. Engineering drawings − mechanical, electrical, civil, etc. - Replacing the blueprints of the past. Typography − The use of character images in publishing - replacing the hard type of the past. Architecture − Construction plans, exterior sketches - replacing the blueprints and hand drawings of the past. Art − Computers provide a new medium for artists. Training − Flight simulators, computer aided instruction, etc. Entertainment − Movies and games. Simulation and modeling − Replacing physical modeling and enactments Transformation means changing some graphics into something else by applying rules. We can have various types of transformations such as translation, scaling up or down, rotation, shearing, etc. When a transformation takes place on a 2D plane, it is called 2D transformation. Transformations play an important role in computer graphics to reposition the graphics on the screen and change their size or orientation. Homogenous Coordinates To perform a sequence of transformation such as translation followed by rotation and scaling, we need to follow a sequential process − • Translation A translation moves an object to a different position on the screen. You can translate a point in 2D by adding translation coordinate (tx, ty) to the original coordinate (X, Y) to get the new coordinate (X’, Y’).

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Rotation In rotation, we rotate the object at particular angle θ (theta) from its origin. From the following figure, we can see that the point P(X, Y) is located at angle φ from the horizontal X coordinate with distance r from the origin. Let us suppose you want to rotate it at the angle θ. After rotating it to a new location, you will get a new point P’ (X’, Y’). Scaling To change the size of an object, scaling transformation is used. In the scaling process, you either expand or compress the dimensions of the object. Scaling can be achieved by multiplying the original coordinates of the object with the scaling factor to get the desired result. Where S is the scaling matrix. The scaling process is shown in the following figure. If we provide values less than 1 to the scaling factor S, then we can reduce the size of the object. If we provide values greater than 1, then we can increase the size of the object. Reflection Reflection is the mirror image of original object. In other words, we can say that it is a rotation operation with 180°. In reflection transformation, the size of the object does not change.

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The following figures show reflections with respect to X and Y axes, and about the origin respectively. Shear A transformation that slants the shape of an object is called the shear transformation. There are two shear transformations X-Shear and Y-Shear. One shifts X coordinates values and other shifts Y coordinate values. However; in both the cases only one coordinate changes its coordinates and other preserves its values. Shearing is also termed as Skewing. X-Shear The X-Shear preserves the Y coordinate and changes are made to X coordinates, which causes the vertical lines to tilt right or left as shown in below figure. Y-Shear The Y-Shear preserves the X coordinates and changes the Y coordinates which causes the horizontal lines to transform into lines which slopes up or down as shown in the following figure.

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