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More Questions from This Interview. Comment hidden because of low score. Click to expand. Add a Comment Add a Comment. Writing Code? Add Question. Improve this answer. Community Bot 1.
The fact that a 4x4 matrix is overkill for a single translation or a single rotation is outweight by the fact that you usually don't just transform a vertex by single translation or a single rotation. Yet the even bigger advantage gained from the uniform way of using a matrix is not only uniformity, but representation of an entire chain of transformations in a single operation.
While that might have been implied, I found it unclear and important enough to mention it explicitly. But the answer was still good anyway, it wasn't a critique. When I said trigonometry, I was implying using it directly, not through a matrix, to generate some simple things. Show 8 more comments. Why is it possible to use matrices to represent rotations?
The only transformations we want to do to on them are rotations and translations. Why is it nice to use matrices at all? This naturally leads to maintaining a stack of matrices: calculate chassis matrix multiply by tire matrix push remove tire matrix pop multiply by driving wheel matrix push How adding one dimension solves the problem Let's consider the case from 1D to 2D which is easier to visualize.
It is cool to visualize this transformation: Image source. Affine space Affine space is the space generated by all our 3D linear transformations matrix multiplications together with the 4D shear 3D translations.
Frustum projection But wait, there is one more important transformation that we do all the time: glFrustum , which makes an object 2x further, appear 2x smaller.
We can verify that for some values, e. The mathematical "trickery" of adding the w and dividing by it is called homogeneous coordinates Image source. I think those who don't already understand would be more likely to understand from my answer, as it is more exemplified and visual.
If you find specific errors or points which are completely irrelevant, point them so I can improve. To address the previous user's concern, the answer should be rearranged to start at "Translations cannot be represented by 3D matrices". This answers the immediate question posed and the OP can continue on to the further well written and enthusiastic details provided; those finer details being what I'm interested in here so I may be biased, but this is certainly not "rambling".
Not sure if it exactly targets the original question, but you get my upvote, sir. Show 1 more comment. Leopd Leopd 1 1 silver badge 3 3 bronze badges. Ray Tayek Ray Tayek 1 1 silver badge 4 4 bronze badges. A succinct explanation is better than only linking to wikipedia. But also for various other purposes. Sounds good? The Overflow Blog. Does ES6 make JavaScript frameworks obsolete? Podcast Do polyglots have an edge when it comes to mastering programming Active 6 years, 8 months ago.
Viewed 8k times. ECS is: Are these translation vectors? Improve this question. Lutz Lehmann Zaay Zaay 1 1 gold badge 7 7 silver badges 18 18 bronze badges. You need to do some study. See, for example stackoverflow. Each line is a row in the matrix; the commas separate the column values in that row. This a transformation matrix. You can't understand it without knowing something about matricies.
You can't avoid matrices and vectors if you're serious about 3d graphics. As for 'why' the use of a 4x4 matrix, this falls under the auspices of homogenous coordinates. Add a comment. Active Oldest Votes. Improve this answer. Thank you for explanation. What does the x between Tz and z stand for?
That's a multiplication operator.
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