Is it necessary to involve relative grid system while object transformations?
Added by Paul D.
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The question is asking whether it is necessary to involve a relative grid system when performing object transformations. Object transformations typically refer to operations like scaling, rotating, or translating objects in a design or development context. Show more…
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Linear transformations have one big drawback: while they can scale, skew, and rotate, they cannot shift objects. Since shifting is an essential operation, in computer graphics it is handled by using something called homogeneous coordinates. Watch the video below to see how they're used: Translations using homogenous coordinates [+] A) In homogenous coordinates, what matrix would be used to shift an object 2 units to the left and 3 units up? B) Now, suppose we had an object and we want to rotate that object 90 degrees counterclockwise around the point (3,4). We can't do this using a regular rotation matrix, since that always rotates about the origin. So instead, we could use a three step process: 1) shift the object so the point (3,4) is moved to the origin, 2) rotate it as desired, 3) shift it back to the original position. Find the matrix that will accomplish this, in homogenous coordinates. Hint: it will be the product of three matrices. Be careful about order. You can test your answer using the widget below the answer entry area.
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