What i am trying to do http://www.youtube.com/watch?v=CaTI2d0tQME 3:15
In my 3D api there is quad.rotation[x,y,z], quad[x,y,z] which is center of it and width/height. I understand that vertices are being calculated from all of the given. And normal can be calculated from vertices but i have a feeling i should be able to get it just from the rotation?
Yes you can !
Your quad must be axis-oriented (along the X, Y or Z axis, which is its normal vector in its local space). Compose this vector with the quad rotation matrix and you will have your new, nice and shiny normal vector in world space !
A little warning : if the quad transformation matrix is generated by any 3D engine, it could contain scaling factors that will mess the normal vector up. In this case, the classical solution is to compute the transposed inverse of the matrix, or to generate your custom transformation matrix with the quad's rotation values.
Related
I have an SVG <path> with points in "model" coordinate system. For simplicity let my path consist of x, sin(x) pairs - note the lack of any scaling and offsets.
To render it on screen I calculated a SVGMatrix and put it into SVGTransformList of my path element. Also I use CSS vector-effect: non-scaling-stroke.
Now I want to pan my sine chart using a mouse, so I got the shift vector in SVG screen coordinates.
My idea is to put one more matrix in my SVGTransformList and calculate it from the screen shift vector.
Should I put this new matrix before or after my original matrix? What is considered a good style? (I know that the coefficients of the second matrix will be different in the two cases)
Also to transform my shift vector to model coordinates I transform back two SVGPoints: zero and with coordinates of my delta vector, and manually subtract the images coordinate-wise. Is it the way to transform vectors, e.g. there are
no better math or API approach?
I'm working on implementing Akush Gupta's synthetic data generation dataset (http://www.robots.ox.ac.uk/~vgg/data/scenetext/gupta16.pdf). In his work. he used a convolutional neural network to extract a point cloud from a 2-dimensional scenery image, segmented the point clouds to isolate different planes, used RANSAC to fit a 3d plane to the point cloud segments, and then warped the pixels for the segment, given the 3D plane, to a fronto-parallel view.
I'm stuck in this last part- warping my extracted 3D plane to a fronto-parallel view. I have X, Y, and Z vectors as well as a normal vector. I'm thinking what I need to do is perform some type of perspective transform or rotation that would bring all the pixels on the plane to a complete 0 Z-axis while the X and Y would remain the same. I could be wrong about this, it's been a long time since I've had any formal training in geometry or linear algebra.
It looks like skimage's Perspective Transform requires me to know the dimensions of the final segment coordinates in 2d space. It looks like AffineTransform requires me to know the rotation. All I have at this point is my X,Y,Z and normal vector and the suspicion that I may know my destination plane by just setting the Z axis to all zeros. I'm not sure if my assumption is correct but I need to be able to warp all the pixels in the segment of interest to fronto-parallel, fit a bounding box, place text inside of it, then warp the final segment back to the original perspective in 3d space.
Any help with how to think about this or implement it would be massively useful.
I understand that to create a shape (let's say a 3D sphere for an example) that I have to first find the vertex locations of the shape and second, use the parametric equation in order to create the x, y, z points of the triangle meshes. I am currently looking at a sample code to create shapes and it appears that after using the parametric equation in order to find the vectors of the triangle meshes, unit normals to the sphere at the vertices are found.
I understand why regular vectors in the first step are used to create the 3D shape and that a normal vector is perpendicular to the shape object, but I don't understand why the unit normal vectors at the vertices are used to create the shapes? What's the purpose of finding the normal of the vectors?
I am not sure I totally understand your question, but one very important use for normals in computer graphics is calculating reflections. For instance, if you're writing a simple raytracer, Lambertian reflectance is quite easy to compute if you know the normal vector where your camera ray intersects a surface. Normals are similarly required for (off the top of my head) the majority of calculations involved in more complex rendering techniques.
I am playing with some models for the game glest.
These models are made up of one or more meshes; each mesh is made up of many frames which describe the position of each vertex for each frame of animation. In the model shown below, the position of each vertex in each wheel in each frame is in an array.
These models have been exported from 3D tools like Blender. Someone somewhere has the originals.
But I am wondering, for simple animation such as a wheel turning, how can you compute the transforms - the steps of rotate, scale and translate, or the matrix that when applied to the previous frame will result in the new frame?
(Obviously not all frames will have such transforms, because they may distort the models and such.)
Also, how can you detect mirroring and other opportunities to reduce the amount of vertex data by applying a matrix and rendering the same vertices again?
Running speed - if its measured in just minutes - won't be a problem.
First off, some assumptions:
You're dealing with 3D affine transformations (linear transformation plus translation).
You have the vertices for each frame in your animation
You can associate at least 4 vertices in a frame with 4 vertices in the next frame
Then you can take 4 vertices as 4D collumn vectors (appending a 1 in each vector's 4th element) in the original space and concatenate them to create a 4x4 matrix, called X. Do the same for their corresponding vectors in the tranformed space and call them Y, which will also be a 4x4 matrix. A little linear algebra provides you with a method to find the 4x4 matrix A that when applied to X gives you Y. Thus:
AX = Y
A = YX-1
Using this to get rotations and scaling is not trivial. However, the rightmost column of A will contain the translation for the object between the successive frames.
I have a class that holds a 4x4 matrix for scaling and translations. How would I implement rotation methods to this class? And should I implement the rotation as a separate matrix?
You can multiply Your current matrix with a rotation matrix. Take a look at http://en.wikipedia.org/wiki/Rotation_matrix
There's a site which I use every time when I need to look up the details of a 3D transformation, called http://www.euclideanspace.com. The particular page on matrix rotations can be found here.
Edit: Rotation around a given axis, look at the axis & angle representation. This page also links to a description on how to translate one representation to another.
If you need to rotate around mutiple axes, simply multiply the corresponding matrices.
Answering the second half of the question, a single 4x4 matrix is perfectly capable of holding a scaling, a translation, and a rotation. So unless you've put special limitations on what sort of 4x4 matrices you can handle, a single 4x4 is a fine for what you want.
As for rotation about an arbitrary vector (as you are asking in comments), look at the "Rotation about an arbitrary vector" section in the Wikipedia article yabcok links to. You will want to extend that to a 4x4 matrix by padding it out with zeros except for the 4,4 (scaling) position, which should be one. Then use matrix multiplication with your scaling/translation 4x4 to generate a new 4x4 matrix.
You want to make sure you find a reference which talks about the right kind of matrix that's used for computer graphics (namely 3D homogeneous coordinates using a 4x4 transformation matrix for rotation/translation/skewing).
See a computer graphics "bible" such as Foley and Van Dam (pg. 213), or one of these:
The Mathematics of the 3D Rotation Matrix
Mathematics of 3D Graphics
MSDN 3D graphics tutorial
SIGGRAPH article about 3D rotation
other page from CProgramming.com
This page has quite a bit of useful information:
http://knol.google.com/k/matrices-for-3d-applications-translation-rotation