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• Camera rotation - First Person Camera using GLM

  - by tempvar

  I've just switched from deprecated opengl functions to using shaders and GLM math library and i'm having a few problems setting up my camera rotations (first person camera). I'll show what i've got setup so far. I'm setting up my ViewMatrix using the glm::lookAt function which takes an eye position, target and up vector // arbitrary pos and target values pos = glm::vec3(0.0f, 0.0f, 10.0f); target = glm::vec3(0.0f, 0.0f, 0.0f); up = glm::vec3(0.0f, 1.0f, 0.0f); m_view = glm::lookAt(pos, target, up); i'm using glm::perspective for my projection and the model matrix is just identity m_projection = glm::perspective(m_fov, m_aspectRatio, m_near, m_far); model = glm::mat4(1.0); I send the MVP matrix to my shader to multiply the vertex position glm::mat4 MVP = camera->getProjection() * camera->getView() * model; // in shader gl_Position = MVP * vec4(vertexPos, 1.0); My camera class has standard rotate and translate functions which call glm::rotate and glm::translate respectively void camera::rotate(float amount, glm::vec3 axis) { m_view = glm::rotate(m_view, amount, axis); } void camera::translate(glm::vec3 dir) { m_view = glm::translate(m_view, dir); } and i usually just use the mouse delta position as the amount for rotation Now normally in my previous opengl applications i'd just setup the yaw and pitch angles and have a sin and cos to change the direction vector using (gluLookAt) but i'd like to be able to do this using GLM and matrices. So at the moment i have my camera set 10 units away from the origin facing that direction. I can see my geometry fine, it renders perfectly. When i use my rotation function... camera->rotate(mouseDeltaX, glm::vec3(0, 1, 0)); What i want is for me to look to the right and left (like i would with manipulating the lookAt vector with gluLookAt) but what's happening is It just rotates the model i'm looking at around the origin, like im just doing a full circle around it. Because i've translated my view matrix, shouldn't i need to translate it to the centre, do the rotation then translate back away for it to be rotating around the origin? Also, i've tried using the rotate function around the x axis to get pitch working, but as soon as i rotate the model about 90 degrees, it starts to roll instead of pitch (gimbal lock?). Thanks for your help guys, and if i've not explained it well, basically i'm trying to get a first person camera working with matrix multiplication and rotating my view matrix is just rotating the model around the origin.

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• glm quaternion camera rotating on wrong axis

  - by Jarrett

  I'm trying to get my camera implemented with a glm::quat used to store the rotation. However, whenever I do circles with the mouse, the camera rotates along the axis I am viewing (i.e. I think it's called the target axis). For example, if I rotated the mouse in a clockwise fashion, the camera rotates clockwise around the axis. I initialize my quaternion like so: void Camera::initialize() { orientationQuaternion_ = glm::quat(); orientationQuaternion_ = glm::normalize(orientationQuaternion_); } I rotate like so: void Camera::rotate(const glm::detail::float32& degrees, const glm::vec3& axis) { orientationQuaternion_ = orientationQuaternion_ * glm::normalize(glm::angleAxis(degrees, axis)); } and I set the viewMatrix like so: void Camera::render() { glm::quat temp = glm::conjugate(orientationQuaternion_); viewMatrix_ = glm::mat4_cast(temp); viewMatrix_ = glm::translate(viewMatrix_, glm::vec3(-pos_.x, -pos_.y, -pos_.z)); } The only axis' I actually try to rotate are the X and Y axis (i.e. (1,0,0) and (0,1,0)). Anyone have any idea why I see my camera rotating around the target axis?

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• Glm Vector Transformations [duplicate]

  - by Reanimation

  This question already has an answer here: Car-like Physics - Basic Maths to Simulate Steering 2 answers I have a cube rendered on the screen which represents a car (or similar). Using Projection/Model matrices and Glm I am able to move it back and fourth along the axes and rotate it left or right. I'm having trouble with the vector mathematics to make the cube move forwards no matter which direction it's current orientation is. (ie. if I would like, if it's rotated right 30degrees, when it's move forwards, it travels along the 30degree angle on a new axes). I hope I've explained that correctly. This is what I've managed to do so far in terms of using glm to move the cube: glm::vec3 vel; //velocity vector void renderMovingCube(){ glUseProgram(movingCubeShader.handle()); GLuint matrixLoc4MovingCube = glGetUniformLocation(movingCubeShader.handle(), "ProjectionMatrix"); glUniformMatrix4fv(matrixLoc4MovingCube, 1, GL_FALSE, &ProjectionMatrix[0][0]); glm::mat4 viewMatrixMovingCube; viewMatrixMovingCube = glm::lookAt(camOrigin, camLookingAt, camNormalXYZ); vel.x = cos(rotX); vel.y=sin(rotX); vel*=moveCube; //move cube ModelViewMatrix = glm::translate(viewMatrixMovingCube,globalPos*vel); //bring ground and cube to bottom of screen ModelViewMatrix = glm::translate(ModelViewMatrix, glm::vec3(0,-48,0)); ModelViewMatrix = glm::rotate(ModelViewMatrix, rotX, glm::vec3(0,1,0)); //manually turn glUniformMatrix4fv(glGetUniformLocation(movingCubeShader.handle(), "ModelViewMatrix"), 1, GL_FALSE, &ModelViewMatrix[0][0]); //pass matrix to shader movingCube.render(); //draw glUseProgram(0); } keyboard input: void keyboard() { char BACKWARD = keys['S']; char FORWARD = keys['W']; char ROT_LEFT = keys['A']; char ROT_RIGHT = keys['D']; if (FORWARD) //W - move forwards { globalPos += vel; //globalPos.z -= moveCube; BACKWARD = false; } if (BACKWARD)//S - move backwards { globalPos.z += moveCube; FORWARD = false; } if (ROT_LEFT)//A - turn left { rotX +=0.01f; ROT_LEFT = false; } if (ROT_RIGHT)//D - turn right { rotX -=0.01f; ROT_RIGHT = false; } Where am I going wrong with my vectors? I would like change the direction of the cube (which it does) but then move forwards in that direction.

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• glm matrix conversion for DirectX

  - by niktehpui

  For on of the coursework specification I need to work with DirectX, so I tried to implement a DirectX Renderer in my small cross-platform framework (to have it optionally available for Windows). Since I want to stick to my dependencies I want use glm for vector/matrix/quaternions math. The vectors seem to be fully compatible with DirectX, but the glm::mat4 is not working properly in DirectX Effects Framework. I assumed the reason is that DirectX uses row majors layouts and OpenGL column majors (although if I remember right internally in HLSL DX uses column major as well), so I transposed the matrix, but I still get no proper results compared to using XNA-Math. XNA-Version of the code (works): XMMATRIX world = XMMatrixIdentity(); XMMATRIX view = XMMatrixLookAtLH(XMVectorSet(5.0, 5.0, 5.0, 1.0f), XMVectorZero(), XMVectorSet(0.0f, 1.0f, 0.0f, 0.0f)); XMMATRIX proj = XMMatrixPerspectiveFovLH(0.25f*3.14f, 1.25f, 1.0f, 1000.0f); XMMATRIX worldViewProj = world*view*proj; m_fxWorldViewProj->SetMatrix(reinterpret_cast<float*>(&worldViewProj)); This works flawlessly and displays the expected colored cube. GLM-Version (does not work): glm::mat4 world(1.0f); glm::mat4 view = glm::lookAt(glm::vec3(5.0f, 5.0f, 5.0f), glm::vec3(0.0f, 0.0f, 0.0f), glm::vec3(0.0f, 1.0f, 0.0f)); glm::mat4 proj = glm::perspective(0.25f*3.14f, 1.25f, 1.0f, 1000.0f); glm::mat4 worldViewProj = glm::transpose(world*view*proj); m_fxWorldViewProj->SetMatrix(glm::value_ptr(worldViewProj)); Displays nothing, screen stays black. I really would like to stick to glm on all platforms.

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• Understanding glm$residuals and resid(glm)

  - by Michael Bishop

  Hi, Can you tell me what is returned by glm$residuals and resid(glm) where glm is a quasipoisson object. e.g. How would I create them using glm$y and glm$linear.predictors. glm$residuals n missing unique Mean .05 .10 .25 .50 .75 .90 .95 37715 10042 2174 -0.2574 -2.7538 -2.2661 -1.4480 -0.4381 0.7542 1.9845 2.7749 lowest : -4.243 -3.552 -3.509 -3.481 -3.464 highest: 8.195 8.319 8.592 9.089 9.416 resid(glm) n missing unique Mean .05 .10 .25 37715 0 2048 -2.727e-10 -1.0000 -1.0000 -0.6276 .50 .75 .90 .95 -0.2080 0.4106 1.1766 1.7333 lowest : -1.0000 -0.8415 -0.8350 -0.8333 -0.8288 highest: 7.2491 7.6110 7.6486 7.9574 10.1932

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• Head Rotation in Opposite Direction with GLM and Oculus Rift SDK

  - by user3434662

  I am 90% there in getting orientation to work. I am just trying to resolve one last bit and I hope someone can point me to any easy errors I am making but not seeing. My code works except when a person looks left the camera actually rotates right. Vice versa with looking right, camera rotates left. Any idea what I am doing wrong here? I retrieve the orientation from the Oculus Rift like so: OVR::Quatf OculusRiftOrientation = PredictedPose.Orientation; glm::vec3 CurrentEulerAngles; glm::quat CurrentOrientation; OculusRiftOrientation.GetEulerAngles<OVR::Axis_X, OVR::Axis_Y, OVR::Axis_Z, OVR::Rotate_CW, OVR::Handed_R> (&CurrentEulerAngles.x, &CurrentEulerAngles.y, &CurrentEulerAngles.z); CurrentOrientation = glm::quat(CurrentEulerAngles); And here is how I calculate the LookAt: /* DirectionOfWhereCameraIsFacing is calculated from mouse and standing position so that you are not constantly rotating after you move your head. */ glm::vec3 DirectionOfWhereCameraIsFacing; glm::vec3 RiftDirectionOfWhereCameraIsFacing; glm::vec3 RiftCenterOfWhatIsBeingLookedAt; glm::vec3 PositionOfEyesOfPerson; glm::vec3 CenterOfWhatIsBeingLookedAt; glm::vec3 CameraPositionDelta; RiftDirectionOfWhereCameraIsFacing = DirectionOfWhereCameraIsFacing; RiftDirectionOfWhereCameraIsFacing = glm::rotate(CurrentOrientation, DirectionOfWhereCameraIsFacing); PositionOfEyesOfPerson += CameraPositionDelta; CenterOfWhatIsBeingLookedAt = PositionOfEyesOfPerson + DirectionOfWhereCameraIsFacing * 1.0f; RiftCenterOfWhatIsBeingLookedAt = PositionOfEyesOfPerson + RiftDirectionOfWhereCameraIsFacing * 1.0f; RiftView = glm::lookAt(PositionOfEyesOfPerson, RiftCenterOfWhatIsBeingLookedAt, DirectionOfUpForPerson);

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• Using OpenGL Mathematics (GLM) in an Objective-C program

  - by user1621592

  i am trying to use GLM to load a .obj object in my Objective-C Program (Xcode 4.4 Mac Os X). I have added the glm folder to my project. i try to import it using #import "glm/glm.hpp", but the program doesn't build. some of the errors are the following: (this errors are produced in the GLM files) namespace glm{ //Unknown type name 'namespace' namespace detail { ..... it doesn't find the cstdlib, cmath, and other libraries.... This happens because my program is in Objective-c and the GLM doesn't work with this language??? How can i resolve this problem??? Thanks for your help.

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• How to raycast select a scaled OBB?

  - by user3254944

  I have the OBB picking code to select an OBB with code inspired from Real time Rendering 3 and opengl-tutorial.org. I can successfully select objects that have been moved or rotated. However, I cant correctly select an object that has been scaled. The bounding box scales right, but the I can only select the object in a thin strip on its center. How do I fix the checkForHits() function to allow it to read the scaling that I passed to it in the raycast matrix? void GLWidget::selectObjRaycast() { glm::vec2 mouse = (glm::vec2(mousePos.x(), mousePos.y()) / glm::vec2(this->width(), this->height())) * 2.0f - 1.0f; mouse.y *= -1; glm::mat4 toWorld = glm::inverse(ProjectionM * ViewM); glm::vec4 from = toWorld * glm::vec4(mouse, -1.0f, 1.0f); glm::vec4 to = toWorld * glm::vec4(mouse, 1.0f, 1.0f); from /= from.w; to /= to.w; fromAABB = glm::vec3(from); toAABB = glm::normalize(glm::vec3(to - from)); checkForHits(); } void GLWidget::checkForHits() { for (int i = 0; i < myWin.myEtc->allObj.size(); ++i) //check for hits on each obj's bb { bool miss = 0; float tMin = 0.0f; float tMax = 100000.0f; glm::vec3 bbPos(myWin.myEtc->allObj[i]->raycastM[3].x, myWin.myEtc->allObj[i]->raycastM[3].y, myWin.myEtc->allObj[i]->raycastM[3].z); glm::vec3 delta = bbPos - fromAABB; for (int j = 0; j < 3; ++j) { glm::vec3 axis(myWin.myEtc->allObj[i]->raycastM[j].x, myWin.myEtc->allObj[i]->raycastM[j].y, myWin.myEtc->allObj[i]->raycastM[j].z); float e = glm::dot(axis, delta); float f = glm::dot(toAABB, axis); if (fabs(f) > 0.001f) { float t1 = (e + myWin.myEtc->allObj[i]->bbMin[j]) / f; float t2 = (e + myWin.myEtc->allObj[i]->bbMax[j]) / f; if (t1 > t2) { float w = t1; t1 = t2; t2 = w; } if (t2 < tMax) tMax = t2; if (t1 > tMin) tMin = t1; if (tMax < tMin) miss = 1; } else { if (-e + myWin.myEtc->allObj[i]->bbMin[j] > 0.0f || -e + myWin.myEtc->allObj[i]->bbMax[j] < 0.0f) miss = 1; } } if (miss == 0) { intersection_distance = tMin; myWin.myEtc->sel.push_back(myWin.myEtc->allObj[i]); myWin.myEtc->allObj[i]->highlight = myWin.myGLHelp->highlight; break; } } } void Object::render(glm::mat4 PV) { scaleM = glm::scale(glm::mat4(), s->val_3); r_quat = glm::quat(glm::radians(r->val_3)); rotationM = glm::toMat4(r_quat); translationM = glm::translate(glm::mat4(), t->val_3); transLocal1M = glm::translate(glm::mat4(), -rsPivot->val_3); transLocal2M = glm::translate(glm::mat4(), rsPivot->val_3); raycastM = translationM * transLocal2M * rotationM * scaleM * transLocal1M; // MVP = PV * translationM * transLocal2M * rotationM * scaleM * transLocal1M; }

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• GLM Velocity Vectors - Basic Maths to Simulate Steering

  - by Reanimation

  UPDATE - Code updated below but still need help adjusting my math. I have a cube rendered on the screen which represents a car (or similar). Using Projection/Model matrices and Glm I am able to move it back and fourth along the axes and rotate it left or right. I'm having trouble with the vector mathematics to make the cube move forwards no matter which direction it's current orientation is. (ie. if I would like, if it's rotated right 30degrees, when it's move forwards, it travels along the 30degree angle on a new axes). I hope I've explained that correctly. This is what I've managed to do so far in terms of using glm to move the cube: glm::vec3 vel; //velocity vector void renderMovingCube(){ glUseProgram(movingCubeShader.handle()); GLuint matrixLoc4MovingCube = glGetUniformLocation(movingCubeShader.handle(), "ProjectionMatrix"); glUniformMatrix4fv(matrixLoc4MovingCube, 1, GL_FALSE, &ProjectionMatrix[0][0]); glm::mat4 viewMatrixMovingCube; viewMatrixMovingCube = glm::lookAt(camOrigin, camLookingAt, camNormalXYZ); vel.x = cos(rotX); vel.y=sin(rotX); vel*=moveCube; //move cube ModelViewMatrix = glm::translate(viewMatrixMovingCube,globalPos*vel); //bring ground and cube to bottom of screen ModelViewMatrix = glm::translate(ModelViewMatrix, glm::vec3(0,-48,0)); ModelViewMatrix = glm::rotate(ModelViewMatrix, rotX, glm::vec3(0,1,0)); //manually turn glUniformMatrix4fv(glGetUniformLocation(movingCubeShader.handle(), "ModelViewMatrix"), 1, GL_FALSE, &ModelViewMatrix[0][0]); //pass matrix to shader movingCube.render(); //draw glUseProgram(0); } keyboard input: void keyboard() { char BACKWARD = keys['S']; char FORWARD = keys['W']; char ROT_LEFT = keys['A']; char ROT_RIGHT = keys['D']; if (FORWARD) //W - move forwards { globalPos += vel; //globalPos.z -= moveCube; BACKWARD = false; } if (BACKWARD)//S - move backwards { globalPos.z += moveCube; FORWARD = false; } if (ROT_LEFT)//A - turn left { rotX +=0.01f; ROT_LEFT = false; } if (ROT_RIGHT)//D - turn right { rotX -=0.01f; ROT_RIGHT = false; } Where am I going wrong with my vectors? I would like change the direction of the cube (which it does) but then move forwards in that direction.

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• Recommended books on math for programmers

  - by Anto

  Some programmers do, besides programming, like math (others don't). What books on math do you recommend programmers who like math to read? There are books which present concepts which are applicable in programming and/or computer science, other books about things which will fascinate programmers etc. Books on applying math to programming are okey, but they should be mainly about math (and not programming). Motivate your answers, with focus on why programmers should read the book(s).

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• Quaternion LookAt for camera

  - by Homar

  I am using the following code to rotate entities to look at points. glm::vec3 forwardVector = glm::normalize(point - position); float dot = glm::dot(glm::vec3(0.0f, 0.0f, 1.0f), forwardVector); float rotationAngle = (float)acos(dot); glm::vec3 rotationAxis = glm::normalize(glm::cross(glm::vec3(0.0f, 0.0f, 1.0f), forwardVector)); rotation = glm::normalize(glm::quat(rotationAxis * rotationAngle)); This works fine for my usual entities. However, when I use this on my Camera entity, I get a black screen. If I flip the subtraction in the first line, so that I take the forward vector to be the direction from the point to my camera's position, then my camera works but naturally my entities rotate to look in the opposite direction of the point. I compute the transformation matrix for the camera and then take the inverse to be the View Matrix, which I pass to my OpenGL shaders: glm::mat4 viewMatrix = glm::inverse( cameraTransform->GetTransformationMatrix() ); The orthographic projection matrix is created using glm::ortho. What's going wrong?

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• Math questions at a programmer interview?

  - by anon

  So I went to an interview at Samsung here in Dallas, Texas. The way the recruiter described the job, he didn't make it sound like it was too math-oriented. The job basically involved graphics programming and C++. Yes, math is implied in graphics programming, especially shaders, but I still wasn't expecting this... The whole interview lasted about an hour and a half and they asked me nothing but math-related questions. They didn't ask me a single programming question, which I found odd. About all they did was ask me how to write certain math routines as a C++ function, but that's about it. What about programming philosophy questions? Design patterns? Code-correctness? Constness? Exception safety? Thread safety? There are a zillion topics that they could have covered. But they didn't. The main concern I have is that they didn't ask any programming questions. This basically implies to me that any programmer who is good at math can get a job here, but they might put out terrible code. Of course, I think I bombed the interview because I haven't used any sort of linear algebra in about a year and I forget math easily if I haven't used it in practice for a while. Are any of my other fellow programmers out there this way? I'm a game programmer too, so this seems especially odd. The more I learn, the more old knowledge that gets "popped" out of my "stack" (memory). My question is: Does this interview seem suspicious? Is this a typical interview that large corporations have? During the interview they told me that Google's interview process is similar. They have multiple, consecutive interviews where the math problems get more advanced.

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• Math questions at a programmer interview?

  - by anon

  So I went to an interview at Samsung here in Dallas, Texas. The way the recruiter described the job, he didn't make it sound like it was too math-oriented. The job basically involved graphics programming and C++. Yes, math is implied in graphics programming, especially shaders, but I still wasn't expecting this... The whole interview lasted about an hour and a half and they asked me nothing but math-related questions. They didn't ask me a single programming question, which I found odd. About all they did was ask me how to write certain math routines as a C++ function, but that's about it. What about programming philosophy questions? Design patterns? Code-correctness? Constness? Exception safety? Thread safety? There are a zillion topics that they could have covered. But they didn't. The main concern I have is that they didn't ask any programming questions. This basically implies to me that any programmer who is good at math can get a job here, but they might put out terrible code. Of course, I think I bombed the interview because I haven't used any sort of linear algebra in about a year and I forget math easily if I haven't used it in practice for a while. Are any of my other fellow programmers out there this way? I'm a game programmer too, so this seems especially odd. The more I learn, the more old knowledge that gets "popped" out of my "stack" (memory). My question is: Does this interview seem suspicious? Is this a typical interview that large corporations have? During the interview they told me that Google's interview process is similar. They have multiple, consecutive interviews where the math problems get more advanced.

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• CPU Architecture and floating-point math

  - by Jo-Herman Haugholt

  I'm trying to wrap my head around some details about how floating point math is performed on the CPU, trying to better understand what data types to use etc. I think I have a fairly good understanding of how integer math is performed. If I've understood correctly, and disregarding SIMD, a 32-bit CPU will generally perform integer math at at least 32-bit precision etc. Is it correct that floating-point math is dependent on the presence of a FPU? And that the FPU on the x86 is 80-bit, so floating point math is performed at this precision unless using SIMD? What about ARM?

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• Math major as a viable degree

  - by Zak O'Keefe

  While I realize there are many topics about CS vs software engineering vs game school programs, I haven't found anything relating to whether pure math degrees (with CS minor and electives) would also be a viable program. By this I mean: Would having a math major, CS minor put one at competitive disadvantage as compared to a pure CS program? This relates specifically to game engine programming, more on the graphics side. Background (for those who care): Currently a math major, CS minor at school and looking to land a career doing graphics engine programming. Admittedly, I love math and if at all possible would like to stay my current program as long as it doesn't put me at a competitive disadvantage trying to land a job post-graduation. That being said, I'm strong in the traditional C/C++ languages, strong concurrent programming skills, and currently produce self-made games for iOS. As an employer, how badly is the math major hurting me? Just want to get some advice from people already in the field!

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• Bad at math, feeling limited

  - by Peter Stain

  Currently I'm a java developer, making websites. I'm really bad at math, in high school I got suspened because of it once. I didn't program then and had no interest in math. I started programming after high school and started feeling that my poor math skills are limiting me. I feel like the programming's not that hard for me. Though web development in general is not that hard, i guess. I've been doing Spring and Hibernate a lot. What i'm trying to ask is : if I understand and can manage these technologies and programming overall, would it mean that I have some higher than average prerequisite for math and details? Would there be any point or would it be easy for me to take some courses in high school math and get a BSc in math maybe? This web development is really starting to feel like not my cup of tea anymore, i would like to do something more interesting. I'm 25 now and feel like stuck. Any help appreciated.

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• What math should all game programmers know?

  - by Tetrad

  Simple enough question: What math should all game programmers have a firm grasp of in order to be successful? I'm not specifically talking about rendering math or anything in the niche areas of game programming, more specifically just things that even game programmers should know about, and if they don't they'll probably find it useful. Note: as there is no one correct answer, this question (and its answers) is a community wiki. Also, if you would like fancy latex math equations, feel free to use http://mathurl.com/.

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• Game Institute Math Courses

  - by W3Geek

  I'm 21 years old and I suck at math, I mean really bad. I don't have the necessary logic to apply it towards programming. I would like to learn the math and logic of applying it. I found Game Institute (http://www.gameinstitute.com) awhile back and heard a lot of praise about them. Are there Math courses any good? Thank you. Edit: My high school was terrible and did not prepare me for any math. I am fairly decent at programming, I just don't have the logic to apply any mathematics to programming, as an example I don't understand the algorithm of finding the size of a user's screen. Yes I have heard of KhanAcademy (http://www.khanacademy.org/) and I have completed a lot of maths on his website but I still don't have the logic to apply any of it to programming.

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• Long term plan of attack to learn math?

  - by zhenka

  I am a web-developer with a desire to expand my skill-set to mathematics relevant to programming. As 2nd career, I am stuck in college doing some of the requirements while working. I was hoping the my education will teach me the needed skills to apply math, however I am quickly finding it to be too much easily-testable breadth-based approach very inefficient for the time invested. For example in my calculus 2 class, the only remotely useful mind expanding experience I had was volumes and areas under the curve. The rest was just monotonous glorified algebra, which while comes easy to me, could be done by software like wolfram alpha within seconds. This is not my idea of learning math. So here I am a frustrated student looking for a way to improve my understanding of math in a way that focuses on application, understanding and maximally removed needless tedium. However I cannot find a good long term study strategy with this approach in mind. So for those of like mind, how would you go about learning the necessary math without worrying too much about stuff a computer can do much better?

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• Quaternion based rotation and pivot position

  - by Michael IV

  I can't figure out how to perform matrix rotation using Quaternion while taking into account pivot position in OpenGL.What I am currently getting is rotation of the object around some point in the space and not a local pivot which is what I want. Here is the code [Using Java] Quaternion rotation method: public void rotateTo3(float xr, float yr, float zr) { _rotation.x = xr; _rotation.y = yr; _rotation.z = zr; Quaternion xrotQ = Glm.angleAxis((xr), Vec3.X_AXIS); Quaternion yrotQ = Glm.angleAxis((yr), Vec3.Y_AXIS); Quaternion zrotQ = Glm.angleAxis((zr), Vec3.Z_AXIS); xrotQ = Glm.normalize(xrotQ); yrotQ = Glm.normalize(yrotQ); zrotQ = Glm.normalize(zrotQ); Quaternion acumQuat; acumQuat = Quaternion.mul(xrotQ, yrotQ); acumQuat = Quaternion.mul(acumQuat, zrotQ); Mat4 rotMat = Glm.matCast(acumQuat); _model = new Mat4(1); scaleTo(_scaleX, _scaleY, _scaleZ); _model = Glm.translate(_model, new Vec3(_pivot.x, _pivot.y, 0)); _model =rotMat.mul(_model);//_model.mul(rotMat); //rotMat.mul(_model); _model = Glm.translate(_model, new Vec3(-_pivot.x, -_pivot.y, 0)); translateTo(_x, _y, _z); notifyTranformChange(); } Model matrix scale method: public void scaleTo(float x, float y, float z) { _model.set(0, x); _model.set(5, y); _model.set(10, z); _scaleX = x; _scaleY = y; _scaleZ = z; notifyTranformChange(); } Translate method: public void translateTo(float x, float y, float z) { _x = x - _pivot.x; _y = y - _pivot.y; _z = z; _position.x = _x; _position.y = _y; _position.z = _z; _model.set(12, _x); _model.set(13, _y); _model.set(14, _z); notifyTranformChange(); } But this method in which I don't use Quaternion works fine: public void rotate(Vec3 axis, float angleDegr) { _rotation.add(axis.scale(angleDegr)); // change to GLM: Mat4 backTr = new Mat4(1.0f); backTr = Glm.translate(backTr, new Vec3(_pivot.x, _pivot.y, 0)); backTr = Glm.rotate(backTr, angleDegr, axis); backTr = Glm.translate(backTr, new Vec3(-_pivot.x, -_pivot.y, 0)); _model =_model.mul(backTr);///backTr.mul(_model); notifyTranformChange(); }

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• (int) Math.floor(x / TILESIZE) or just (int) (x / TILESIZE)

  - by Aidan Mueller

  I have a Array that stores my map data and my Tiles are 64X64. Sometimes I need to convert from pixels to units of tiles. So I was doing: int x int y public void myFunction() { getTile((int) Math.floor(x / 64), (int) Math.floor(y / 64)).doOperation(); } But I discovered by using (I'm using java BTW) System.out.println((int) (1 / 1.5)) that converting to an int automatically rounds down. This means that I can replace the (int) Math.floor with just x / 64. But if I run this on a different OS do you think it might give a different result? I'm just afraid there might be some case where this would round up and not down. Should I keep doing it the way I was and maybe make a function like convert(int i) to make it easier? Or is it OK to just do x / 64?

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• Simple Math Multiplayer game - is Ajax sufficient?

  - by Christian Strang

  I'm planning to create a simple math multiplayer game and I plan to just use Ajax for the server/client communication but I'm not sure if this is sufficient or if I need a socket server. The game will look like this: 2-4 users all get a simple math task (like: "37 + 14") they have to solve it as fast as possible first user who solves it is the winner I will track the time for each user, since the game started, on the client side and everytime a user gives an answer, the answer and the passed time will be send to the server. Additionally I'll add a function which will check every 3 seconds if the other users finished, how much time they needed and who won. Do you think this is possible just using Ajax? What alternatives are there?

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• Is there an easy way to type in common math symbols?

  - by srcspider

  Disclaimer: I'm sure someone is going to moan about easy-of-use, for the purpose of this question consider readability to be the only factor that matters So I found this site that converts to easting northing, it's not really important what that even means but here's how the piece of javascript looks. /** * Convert Ordnance Survey grid reference easting/northing coordinate to (OSGB36) latitude/longitude * * @param {OsGridRef} gridref - easting/northing to be converted to latitude/longitude * @returns {LatLonE} latitude/longitude (in OSGB36) of supplied grid reference */ OsGridRef.osGridToLatLong = function(gridref) { var E = gridref.easting; var N = gridref.northing; var a = 6377563.396, b = 6356256.909; // Airy 1830 major & minor semi-axes var F0 = 0.9996012717; // NatGrid scale factor on central meridian var f0 = 49*Math.PI/180, ?0 = -2*Math.PI/180; // NatGrid true origin var N0 = -100000, E0 = 400000; // northing & easting of true origin, metres var e2 = 1 - (b*b)/(a*a); // eccentricity squared var n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n; // n, n², n³ var f=f0, M=0; do { f = (N-N0-M)/(a*F0) + f; var Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (f-f0); var Mb = (3*n + 3*n*n + (21/8)*n3) * Math.sin(f-f0) * Math.cos(f+f0); var Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(f-f0)) * Math.cos(2*(f+f0)); var Md = (35/24)*n3 * Math.sin(3*(f-f0)) * Math.cos(3*(f+f0)); M = b * F0 * (Ma - Mb + Mc - Md); // meridional arc } while (N-N0-M >= 0.00001); // ie until < 0.01mm var cosf = Math.cos(f), sinf = Math.sin(f); var ? = a*F0/Math.sqrt(1-e2*sinf*sinf); // nu = transverse radius of curvature var ? = a*F0*(1-e2)/Math.pow(1-e2*sinf*sinf, 1.5); // rho = meridional radius of curvature var ?2 = ?/?-1; // eta = ? var tanf = Math.tan(f); var tan2f = tanf*tanf, tan4f = tan2f*tan2f, tan6f = tan4f*tan2f; var secf = 1/cosf; var ?3 = ?*?*?, ?5 = ?3*?*?, ?7 = ?5*?*?; var VII = tanf/(2*?*?); var VIII = tanf/(24*?*?3)*(5+3*tan2f+?2-9*tan2f*?2); var IX = tanf/(720*?*?5)*(61+90*tan2f+45*tan4f); var X = secf/?; var XI = secf/(6*?3)*(?/?+2*tan2f); var XII = secf/(120*?5)*(5+28*tan2f+24*tan4f); var XIIA = secf/(5040*?7)*(61+662*tan2f+1320*tan4f+720*tan6f); var dE = (E-E0), dE2 = dE*dE, dE3 = dE2*dE, dE4 = dE2*dE2, dE5 = dE3*dE2, dE6 = dE4*dE2, dE7 = dE5*dE2; f = f - VII*dE2 + VIII*dE4 - IX*dE6; var ? = ?0 + X*dE - XI*dE3 + XII*dE5 - XIIA*dE7; return new LatLonE(f.toDegrees(), ?.toDegrees(), GeoParams.datum.OSGB36); } I found that to be a really nice way of writing an algorythm, at least as far as redability is concerned. Is there any way to easily write the special symbols. And by easily write I mean NOT copy/paste them.

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• how to make a function recursive

  - by tom smith

  i have this huge function and i am wondering how to make it recursive. i have the base case which should never come true, so it should always go to else and keep calling itself with the variable t increases. any help would be great thanks def draw(x, y, t, planets): if 'Satellites' in planets["Moon"]: print ("fillcircle", x, y, planets["Moon"]['Radius']*scale) else: while True: print("refresh") print("colour 0 0 0") print("clear") print("colour 255 255 255") print("fillcircle",x,y,planets['Sun']['Radius']*scale) print("text ", "\"Sun\"",x+planets['Sun']['Radius']*scale,y) if "Mercury" in planets: r_Mercury=planets['Mercury']['Orbital Radius']*scale; print("circle",x,y,r_Mercury) r_Xmer=x+math.sin(t*2*math.pi/planets['Mercury']['Period'])*r_Mercury r_Ymer=y+math.cos(t*2*math.pi/planets['Mercury']['Period'])*r_Mercury print("fillcircle",r_Xmer,r_Ymer,3) print("text ", "\"Mercury\"",r_Xmer+planets['Mercury']['Radius']*scale,r_Ymer) if "Venus" in planets: r_Venus=planets['Venus']['Orbital Radius']*scale; print("circle",x,y,r_Venus) r_Xven=x+math.sin(t*2*math.pi/planets['Venus']['Period'])*r_Venus r_Yven=y+math.cos(t*2*math.pi/planets['Venus']['Period'])*r_Venus print("fillcircle",r_Xven,r_Yven,3) print("text ", "\"Venus\"",r_Xven+planets['Venus']['Radius']*scale,r_Yven) if "Earth" in planets: r_Earth=planets['Earth']['Orbital Radius']*scale; print("circle",x,y,r_Earth) r_Xe=x+math.sin(t*2*math.pi/planets['Earth']['Period'])*r_Earth r_Ye=y+math.cos(t*2*math.pi/planets['Earth']['Period'])*r_Earth print("fillcircle",r_Xe,r_Ye,3) print("text ", "\"Earth\"",r_Xe+planets['Earth']['Radius']*scale,r_Ye) if "Moon" in planets: r_Moon=planets['Moon']['Orbital Radius']*scale; print("circle",r_Xe,r_Ye,r_Moon) r_Xm=r_Xe+math.sin(t*2*math.pi/planets['Moon']['Period'])*r_Moon r_Ym=r_Ye+math.cos(t*2*math.pi/planets['Moon']['Period'])*r_Moon print("fillcircle",r_Xm,r_Ym,3) print("text ", "\"Moon\"",r_Xm+planets['Moon']['Radius']*scale,r_Ym) if "Mars" in planets: r_Mars=planets['Mars']['Orbital Radius']*scale; print("circle",x,y,r_Mars) r_Xmar=x+math.sin(t*2*math.pi/planets['Mars']['Period'])*r_Mars r_Ymar=y+math.cos(t*2*math.pi/planets['Mars']['Period'])*r_Mars print("fillcircle",r_Xmar,r_Ymar,3) print("text ", "\"Mars\"",r_Xmar+planets['Mars']['Radius']*scale,r_Ymar) if "Phobos" in planets: r_Phobos=planets['Phobos']['Orbital Radius']*scale; print("circle",r_Xmar,r_Ymar,r_Phobos) r_Xpho=r_Xmar+math.sin(t*2*math.pi/planets['Phobos']['Period'])*r_Phobos r_Ypho=r_Ymar+math.cos(t*2*math.pi/planets['Phobos']['Period'])*r_Phobos print("fillcircle",r_Xpho,r_Ypho,3) print("text ", "\"Phobos\"",r_Xpho+planets['Phobos']['Radius']*scale,r_Ypho) if "Deimos" in planets: r_Deimos=planets['Deimos']['Orbital Radius']*scale; print("circle",r_Xmar,r_Ymar,r_Deimos) r_Xdei=r_Xmar+math.sin(t*2*math.pi/planets['Deimos']['Period'])*r_Deimos r_Ydei=r_Ymar+math.cos(t*2*math.pi/planets['Deimos']['Period'])*r_Deimos print("fillcircle",r_Xdei,r_Ydei,3) print("text ", "\"Deimos\"",r_Xpho+planets['Deimos']['Radius']*scale,r_Ydei) if "Ceres" in planets: r_Ceres=planets['Ceres']['Orbital Radius']*scale; print("circle",x,y,r_Ceres) r_Xcer=x+math.sin(t*2*math.pi/planets['Ceres']['Period'])*r_Ceres r_Ycer=y+math.cos(t*2*math.pi/planets['Ceres']['Period'])*r_Ceres print("fillcircle",r_Xcer,r_Ycer,3) print("text ", "\"Ceres\"",r_Xcer+planets['Ceres']['Radius']*scale,r_Ycer) if "Jupiter" in planets: r_Jupiter=planets['Jupiter']['Orbital Radius']*scale; print("circle",x,y,r_Jupiter) r_Xjup=x+math.sin(t*2*math.pi/planets['Jupiter']['Period'])*r_Jupiter r_Yjup=y+math.cos(t*2*math.pi/planets['Jupiter']['Period'])*r_Jupiter print("fillcircle",r_Xjup,r_Yjup,3) print("text ", "\"Jupiter\"",r_Xjup+planets['Jupiter']['Radius']*scale,r_Yjup) if "Io" in planets: r_Io=planets['Io']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Io) r_Xio=r_Xjup+math.sin(t*2*math.pi/planets['Io']['Period'])*r_Io r_Yio=r_Yjup+math.cos(t*2*math.pi/planets['Io']['Period'])*r_Io print("fillcircle",r_Xio,r_Yio,3) print("text ", "\"Io\"",r_Xio+planets['Io']['Radius']*scale,r_Yio) if "Europa" in planets: r_Europa=planets['Europa']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Europa) r_Xeur=r_Xjup+math.sin(t*2*math.pi/planets['Europa']['Period'])*r_Europa r_Yeur=r_Yjup+math.cos(t*2*math.pi/planets['Europa']['Period'])*r_Europa print("fillcircle",r_Xeur,r_Yeur,3) print("text ", "\"Europa\"",r_Xeur+planets['Europa']['Radius']*scale,r_Yeur) if "Ganymede" in planets: r_Ganymede=planets['Ganymede']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Ganymede) r_Xgan=r_Xjup+math.sin(t*2*math.pi/planets['Ganymede']['Period'])*r_Ganymede r_Ygan=r_Yjup+math.cos(t*2*math.pi/planets['Ganymede']['Period'])*r_Ganymede print("fillcircle",r_Xgan,r_Ygan,3) print("text ", "\"Ganymede\"",r_Xgan+planets['Ganymede']['Radius']*scale,r_Ygan) if "Callisto" in planets: r_Callisto=planets['Callisto']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Callisto) r_Xcal=r_Xjup+math.sin(t*2*math.pi/planets['Callisto']['Period'])*r_Callisto r_Ycal=r_Yjup+math.cos(t*2*math.pi/planets['Callisto']['Period'])*r_Callisto print("fillcircle",r_Xcal,r_Ycal,3) print("text ", "\"Callisto\"",r_Xcal+planets['Callisto']['Radius']*scale,r_Ycal) if "Saturn" in planets: r_Saturn=planets['Saturn']['Orbital Radius']*scale; print("circle",x,y,r_Saturn) r_Xsat=x+math.sin(t*2*math.pi/planets['Saturn']['Period'])*r_Saturn r_Ysat=y+math.cos(t*2*math.pi/planets['Saturn']['Period'])*r_Saturn print("fillcircle",r_Xsat,r_Ysat,3) print("text ", "\"Saturn\"",r_Xsat+planets['Saturn']['Radius']*scale,r_Ysat) if "Mimas" in planets: r_Mimas=planets['Mimas']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Mimas) r_Xmim=r_Xsat+math.sin(t*2*math.pi/planets['Mimas']['Period'])*r_Mimas r_Ymim=r_Ysat+math.cos(t*2*math.pi/planets['Mimas']['Period'])*r_Mimas print("fillcircle",r_Xmim,r_Ymim,3) print("text ", "\"Mimas\"",r_Xmim+planets['Mimas']['Radius']*scale,r_Ymim) if "Enceladus" in planets: r_Enceladus=planets['Enceladus']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Enceladus) r_Xenc=r_Xsat+math.sin(t*2*math.pi/planets['Enceladus']['Period'])*r_Enceladus r_Yenc=r_Ysat+math.cos(t*2*math.pi/planets['Enceladus']['Period'])*r_Enceladus print("fillcircle",r_Xenc,r_Yenc,3) print("text ", "\"Enceladus\"",r_Xenc+planets['Enceladus']['Radius']*scale,r_Yenc) if "Tethys" in planets: r_Tethys=planets['Tethys']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Tethys) r_Xtet=r_Xsat+math.sin(t*2*math.pi/planets['Tethys']['Period'])*r_Tethys r_Ytet=r_Ysat+math.cos(t*2*math.pi/planets['Tethys']['Period'])*r_Tethys print("fillcircle",r_Xtet,r_Ytet,3) print("text ", "\"Tethys\"",r_Xtet+planets['Tethys']['Radius']*scale,r_Ytet) if "Dione" in planets: r_Dione=planets['Dione']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Dione) r_Xdio=r_Xsat+math.sin(t*2*math.pi/planets['Dione']['Period'])*r_Dione r_Ydio=r_Ysat+math.cos(t*2*math.pi/planets['Dione']['Period'])*r_Dione print("fillcircle",r_Xdio,r_Ydio,3) print("text ", "\"Dione\"",r_Xdio+planets['Dione']['Radius']*scale,r_Ydio) if "Rhea" in planets: r_Rhea=planets['Rhea']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Rhea) r_Xrhe=r_Xsat+math.sin(t*2*math.pi/planets['Rhea']['Period'])*r_Rhea r_Yrhe=r_Ysat+math.cos(t*2*math.pi/planets['Rhea']['Period'])*r_Rhea print("fillcircle",r_Xrhe,r_Yrhe,3) print("text ", "\"Rhea\"",r_Xrhe+planets['Rhea']['Radius']*scale,r_Yrhe) if "Titan" in planets: r_Titan=planets['Titan']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Titan) r_Xtit=r_Xsat+math.sin(t*2*math.pi/planets['Titan']['Period'])*r_Titan r_Ytit=r_Ysat+math.cos(t*2*math.pi/planets['Titan']['Period'])*r_Titan print("fillcircle",r_Xtit,r_Ytit,3) print("text ", "\"Titan\"",r_Xtit+planets['Titan']['Radius']*scale,r_Ytit) if "Iapetus" in planets: r_Iapetus=planets['Iapetus']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Iapetus) r_Xiap=r_Xsat+math.sin(t*2*math.pi/planets['Iapetus']['Period'])*r_Iapetus r_Yiap=r_Ysat+math.cos(t*2*math.pi/planets['Iapetus']['Period'])*r_Iapetus print("fillcircle",r_Xiap,r_Yiap,3) print("text ", "\"Iapetus\"",r_Xiap+planets['Iapetus']['Radius']*scale,r_Yiap) if "Uranus" in planets: r_Uranus=planets['Uranus']['Orbital Radius']*scale; print("circle",x,y,r_Uranus) r_Xura=x+math.sin(t*2*math.pi/planets['Uranus']['Period'])*r_Uranus r_Yura=y+math.cos(t*2*math.pi/planets['Uranus']['Period'])*r_Uranus print("fillcircle",r_Xura,r_Yura,3) print("text ", "\"Uranus\"",r_Xura+planets['Uranus']['Radius']*scale,r_Yura) if "Puck" in planets: r_Puck=planets['Puck']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Puck) r_Xpuc=r_Xura+math.sin(t*2*math.pi/planets['Puck']['Period'])*r_Puck r_Ypuc=r_Yura+math.cos(t*2*math.pi/planets['Puck']['Period'])*r_Puck print("fillcircle",r_Xpuc,r_Ypuc,3) print("text ", "\"Puck\"",r_Xpuc+planets['Puck']['Radius']*scale,r_Ypuc) if "Miranda" in planets: r_Miranda=planets['Miranda']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Miranda) r_Xmira=r_Xura+math.sin(t*2*math.pi/planets['Miranda']['Period'])*r_Miranda r_Ymira=r_Yura+math.cos(t*2*math.pi/planets['Miranda']['Period'])*r_Miranda print("fillcircle",r_Xmira,r_Ymira,3) print("text ", "\"Miranda\"",r_Xmira+planets['Miranda']['Radius']*scale,r_Ymira) if "Ariel" in planets: r_Ariel=planets['Ariel']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Ariel) r_Xari=r_Xura+math.sin(t*2*math.pi/planets['Ariel']['Period'])*r_Ariel r_Yari=r_Yura+math.cos(t*2*math.pi/planets['Ariel']['Period'])*r_Ariel print("fillcircle",r_Xari,r_Yari,3) print("text ", "\"Ariel\"",r_Xari+planets['Ariel']['Radius']*scale,r_Yari) if "Umbriel" in planets: r_Umbriel=planets['Umbriel']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Umbriel) r_Xumb=r_Xura+math.sin(t*2*math.pi/planets['Umbriel']['Period'])*r_Umbriel r_Yumb=r_Yura+math.cos(t*2*math.pi/planets['Umbriel']['Period'])*r_Umbriel print("fillcircle",r_Xumb,r_Yumb,3) print("text ", "\"Umbriel\"",r_Xumb+planets['Umbriel']['Radius']*scale,r_Yumb) if "Titania" in planets: r_Titania=planets['Titania']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Titania) r_Xtita=r_Xura+math.sin(t*2*math.pi/planets['Titania']['Period'])*r_Titania r_Ytita=r_Yura+math.cos(t*2*math.pi/planets['Titania']['Period'])*r_Titania print("fillcircle",r_Xtita,r_Ytita,3) print("text ", "\"Titania\"",r_Xtita+planets['Titania']['Radius']*scale,r_Ytita) if "Oberon" in planets: r_Oberon=planets['Oberon']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Oberon) r_Xober=r_Xura+math.sin(t*2*math.pi/planets['Oberon']['Period'])*r_Oberon r_Yober=r_Yura+math.cos(t*2*math.pi/planets['Oberon']['Period'])*r_Oberon print("fillcircle",r_Xober,r_Yober,3) print("text ", "\"Oberon\"",r_Xober+planets['Oberon']['Radius']*scale,r_Yober) if "Neptune" in planets: r_Neptune=planets['Neptune']['Orbital Radius']*scale; print("circle",x,y,r_Neptune) r_Xnep=x+math.sin(t*2*math.pi/planets['Neptune']['Period'])*r_Neptune r_Ynep=y+math.cos(t*2*math.pi/planets['Neptune']['Period'])*r_Neptune print("fillcircle",r_Xnep,r_Ynep,3) print("text ", "\"Neptune\"",r_Xnep+planets['Neptune']['Radius']*scale,r_Ynep) if "Titan" in planets: r_Titan=planets['Titan']['Orbital Radius']*scale; print("circle",r_Xnep,r_Ynep,r_Titan) r_Xtita=r_Xnep+math.sin(t*2*math.pi/planets['Titan']['Period'])*r_Titan r_Ytita=r_Ynep+math.cos(t*2*math.pi/planets['Titan']['Period'])*r_Titan print("fillcircle",r_Xtita,r_Ytita,3) print("text ", "\"Titan\"",r_Xtita+planets['Titan']['Radius']*scale,r_Ytita) t += 0.003 print(draw(x, y, t, planets))

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• How to learn the math behind the code?

  - by Solomon Wise

  I am a 12 year old who has recently gotten into programming. (Although I know that the number of books you have read does not determine your programming competency or ability, just to paint a "map" of where I am in terms of the content I know...) I've finished the books: Python 3 For Absolute Beginners Pro Python Python Standard Library by Example Beautiful Code Agile Web Development With Rails and am about halfway into Programming Ruby. I have written many small programs (One that finds which files have been updated and deleted in a directory, one that compares multiple players' fantasy baseball value, and some text based games, and many more). Obviously, as I'm not some sort of child prodigy, I can't take a formal Computer Science course until high school. I really want to learn computer science to increase my knowledge about the code, and the how the code runs. I've really become interested in the math part after reading the source code for Python's random module. Is there a place where I can learn CS, or programming math online for free, at a level that would be at least partially understandable to a person my age?

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