Computer Graphics Program For 2D Transformation
Computer Graphics Program For 2D Transformation' title='Computer Graphics Program For 2D Transformation' />Free tutorials for modern Opengl 3. CC. Angel c. 1. Computer graphics is concerned with all aspects of producing pictures or images using a computer the ultimate aim is to represent an imagined world as a. Offering shareware and freeware downloads, drivers, with reviews, to improve your computers performance for beginner to advanced users as well a message forum. Master in Computer Science degrees, programs, and classes at the University of Texas at Tyler, which is part of the renowned University of Texas system. Campuses in. Tutorial 3 Matrices. Canon Lbp 2900 Driver For Windows Xp. The engines dont move the ship at all. The ship stays where it is and the engines move the universe around it. Futurama. This is the single most important tutorial of the whole set. Be sure to read it at least eight times. Homogeneous coordinates. Until then, we only considered 3. D vertices as a x,y,z triplet. Lets introduce w. We will now have x,y,z,w vectors. CS 101 Computing Concepts Credits 5. A broad beginning level survey of computer science concepts. Topics include history of computing, computer hardware. This will be more clear soon, but for now, just remember this If w 1, then the vector x,y,z,1 is a position in space. If w 0, then the vector x,y,z,0 is a direction. In fact, remember this forever. What difference does this make Well, for a rotation, it doesnt change anything. When you rotate a point or a direction, you get the same result. However, for a translation when you move the point in a certain direction, things are different. What could mean translate a direction Not much. Homogeneous coordinates allow us to use a single mathematical formula to deal with these two cases. Transformation matrices. An introduction to matrices. Simply put, a matrix is an array of numbers with a predefined number of rows and colums. For instance, a 2x. In 3. D graphics we will mostly use 4x. They will allow us to transform our x,y,z,w vertices. This is done by multiplying the vertex with the matrix Matrix x Vertex in this order Transformed. Vertex. This isnt as scary as it looks. Put your left finger on the a, and your right finger on the x. This is ax. Move your left finger to the next number b, and your right finger to the next number y. Youve got by. Once again cz. Once again dw. ax by cz dw. Youve got your new x Do the same for each line, and youll get your new x,y,z,w vector. Now this is quite boring to compute, an we will do this often, so lets ask the computer to do it instead. In C, with GLM glm mat. Matrix glm vec. Vector fill my. D+Transformation+Translation+Rotation.jpg' alt='Computer Graphics Program For 2D Transformation' title='Computer Graphics Program For 2D Transformation' />Matrix and my. Vector somehow. Vectormy. Matrixmy. Vector Again, in this order In GLSL mat. Matrix vec. 4my. Vector fill my. Matrix and my. Vector somehow. Vectormy. Matrixy. Vector Yeah, its pretty much the same than GLM. Translation matrices. These are the most simple tranformation matrices to understand. A translation matrix look like this where X,Y,Z are the values that you want to add to your position. So if we want to translate the vector 1. X direction, we get do it Remember, the 1 means that it is a position, not a direction. So our transformation didnt change the fact that we were dealing with a position, which is good. Lets now see what happens to a vector that represents a direction towards the z axis 0,0, 1,0 ie our original 0,0, 1,0 direction, which is great because as I said ealier, moving a direction does not make sense. So, how does this translate to code In C, with GLM include lt glmgtxtransform. Matrixglm translateglm mat. Vector1. 0. 0f,1. Vectormy. Matrixy. Vector guess the result. In GLSL vec. 4transformed. Vectormy. Matrixy. Vector Well, in fact, you almost never do this in GLSL. Most of the time, you use glm translate in C to compute your matrix, send it to GLSL, and do only the multiplication The Identity matrix. This one is special. It doesnt do anything. But I mention it because its as important as knowing that multiplying A by 1. A. In C glm mat. Identity. Matrixglm mat. Scaling matrices. Scaling matrices are quite easy too So if you want to scale a vector position or direction, it doesnt matter by 2. You may ask what is the meaning of scaling a direction Well, often, not much, so you usually dont do such a thing, but in some rare cases it can be handy. X,Y,Z 1,1,1. Its also a special case of translation matrix with X,Y,Z0,0,0, by the wayIn C Use include lt glmgtcmatrixtransform. Scaling. Matrixglm scale2. Rotation matrices. These are quite complicated. Ill skip the details here, as its not important to know their exact layout for everyday use. Th Maths Formulas Pdf here. For more information, please have a look to the Matrices and Quaternions FAQ popular resource, probably available in your language as well. You can also have a look at the Rotations tutorials. Stroke Engine Ppt on this page. In C Use include lt glmgtcmatrixtransform. Rotation. Axis, glm rotateangleindegrees,my. Rotation. Axis Cumulating transformations. So now we know how to rotate, translate, and scale our vectors. It would be great to combine these transformations. This is done by multiplying the matrices together, for instance Transformed. VectorTranslation. Matrixotation. Matrixcale. Matrixriginal. Vector BEWARE This lines actually performs the scaling FIRST, and THEN the rotation, and THEN the translation. This is how matrix multiplication works. Writing the operations in another order wouldnt produce the same result. Try it yourself make one step ahead beware of your computer and turn left turn left, and make one step ahead. As a matter of fact, the order above is what you will usually need for game characters and other items Scale it first if needed then set its direction, then translate it. For instance, given a ship model rotations have been removed for simplification The wrong way. You translate the ship by 1. Its center is now at 1. You scale your ship by 2. Every coordinate is multiplied by 2 relative to the origin, which is far away So you end up with a big ship, but centered at 2. Which you dont want. The right way. You scale your ship by 2. You get a big ship, centered on the origin. You translate your ship. Its still the same size, and at the right distance. Matrix matrix multiplication is very similar to matrix vector multiplication, so Ill once again skip some details and redirect you the the Matrices and Quaternions FAQ if needed. For now, well simply ask the computer to do it in C, with GLM glm mat. Model. Matrixmy. Translation. Matrixy. Rotation. Matrixy. Scale. Matrix glm vec. Transformed. Vectormy. Model. Matrixy. Original. Vector in GLSL mat. The Model, View and Projection matrices. For the rest of this tutorial, we will suppose that we know how to draw Blenders favourite 3d model the monkey Suzanne. The Model, View and Projection matrices are a handy tool to separate transformations cleanly. You may not use this after all, thats what we did in tutorials 1 and 2. But you should. This is the way everybody does, because its easier this way. The Model matrix. This model, just as our beloved red triangle, is defined by a set of vertices. The X,Y,Z coordinates of these vertices are defined relative to the objects center that is, if a vertex is at 0,0,0, it is at the center of the object. Wed like to be able to move this model, maybe because the player controls it with the keyboard and the mouse. Easy, you just learnt do do so translationotationcale, and done. You apply this matrix to all your vertices at each frame in GLSL, not in C and everything moves. Something that doesnt move will be at the center of the world. Your vertices are now in World Space. This is the meaning of the black arrow in the image below We went from Model Space all vertices defined relatively to the center of the model to World Space all vertices defined relatively to the center of the world. We can sum this up with the following diagram The View matrix. Lets quote Futurama again The engines dont move the ship at all.