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• Determine arc-length of a Catmull-Rom spline

  - by Wouter

  I have a path that is defined by a concatenation of Catmull-Rom splines. I use the static method Vector2.CatmullRom in XNA that allows for interpolation between points with a value going from 0 to 1. Not every spline in this path has the same length. This causes speed differences if I let the weight go at a constant speed for every spline while proceeding along the path. I can remedy this by letting the speed of the weight be dependent on the length of the spline. How can I determine the length of such a spline? Should I just approximate by cutting the spline into 10 straight lines and sum their lengths? I'm using this for dynamic texture mapping on a generated mesh defined by splines.

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• 2d movement solution

  - by Phil

  Hi! I'm making a simple top-down tank game on the ipad where the user controls the movement of the tank with the left "joystick" and the rotation of the turret with the right one. I've spent several hours just trying to get it to work decently but now I turn to the pros :) I have two referencial objects, one for the movement and one for the rotation. The referencial objects always stay max two units away from the tank and I use them to tell the tank in what direction to move. I chose this approach to decouple movement and rotational behaviour from the raw input of the joysticks, I believe this will make it simpler to implement whatever behaviour I want for the tank. My problem is 1; the turret rotates the long way to the target. With this I mean that the target can be -5 degrees away in rotation and still it rotates 355 degrees instead of -5 degrees. I can't figure out why. The other problem is with the movement. It just doesn't feel right to have the tank turn while moving. I'd like to have a solution that would work as well for the AI as for the player. A blackbox function for the movement where the player only specifies in what direction it should move and it moves there under the constraints that are imposed on it. I am using the standard joystick class found in the Unity iPhone package. This is the code I'm using for the movement: public class TankFollow : MonoBehaviour { //Check angle difference and turn accordingly public GameObject followPoint; public float speed; public float turningSpeed; void Update() { transform.position = Vector3.Slerp(transform.position, followPoint.transform.position, speed * Time.deltaTime); //Calculate angle var forwardA = transform.forward; var forwardB = (followPoint.transform.position - transform.position); var angleA = Mathf.Atan2(forwardA.x, forwardA.z) * Mathf.Rad2Deg; var angleB = Mathf.Atan2(forwardB.x, forwardB.z) * Mathf.Rad2Deg; var angleDiff = Mathf.DeltaAngle(angleA, angleB); //print(angleDiff.ToString()); if (angleDiff > 5) { //Rotate to transform.Rotate(new Vector3(0, (-turningSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); } else if (angleDiff < 5) { transform.Rotate(new Vector3(0, (turningSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); } else { } transform.position = new Vector3(transform.position.x, 0, transform.position.z); } } And this is the code I'm using to rotate the turret: void LookAt() { var forwardA = -transform.right; var forwardB = (toLookAt.transform.position - transform.position); var angleA = Mathf.Atan2(forwardA.x, forwardA.z) * Mathf.Rad2Deg; var angleB = Mathf.Atan2(forwardB.x, forwardB.z) * Mathf.Rad2Deg; var angleDiff = Mathf.DeltaAngle(angleA, angleB); //print(angleDiff.ToString()); if (angleDiff - 180 > 1) { //Rotate to transform.Rotate(new Vector3(0, (turretSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); } else if (angleDiff - 180 < -1) { transform.Rotate(new Vector3(0, (-turretSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); print((angleDiff - 180).ToString()); } else { } } Since I want the turret reference point to turn in relation to the tank (when you rotate the body, the turret should follow and not stay locked on since it makes it impossible to control when you've got two thumbs to work with), I've made the TurretFollowPoint a child of the Turret object, which in turn is a child of the body. I'm thinking that I'm making it too difficult for myself with the reference points but I'm imagining that it's a good idea. Please be honest about this point. So I'll be grateful for any help I can get! I'm using Unity3d iPhone. Thanks!

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• Finding the normal of OBB face with an OBB penetrating

  - by Milo

  Below is an illustration: I have an OBB in an OBB (see below for OBB2D code if needed). What I need to determine is, what face it is in, and what direction do I point the normal? The goal is to get the OBB out of the OBB so the normal needs to face outward of the OBB. How could I go about: Finding what face the line is penetrating given the 4 corners of the OBB and the class below: if we define dx=x2-x1 and dy=y2-y1, then the normals are (-dy, dx) and (dy, -dx). Which normal points outward of the OBB? Thanks public class OBB2D { // Corners of the box, where 0 is the lower left. private Vector2D corner[] = new Vector2D[4]; private Vector2D center = new Vector2D(); private Vector2D extents = new Vector2D(); private RectF boundingRect = new RectF(); private float angle; //Two edges of the box extended away from corner[0]. private Vector2D axis[] = new Vector2D[2]; private double origin[] = new double[2]; public OBB2D(Vector2D center, float w, float h, float angle) { set(center,w,h,angle); } public OBB2D(float left, float top, float width, float height) { set(new Vector2D(left + (width / 2), top + (height / 2)),width,height,0.0f); } public void set(Vector2D center,float w, float h,float angle) { Vector2D X = new Vector2D( (float)Math.cos(angle), (float)Math.sin(angle)); Vector2D Y = new Vector2D((float)-Math.sin(angle), (float)Math.cos(angle)); X = X.multiply( w / 2); Y = Y.multiply( h / 2); corner[0] = center.subtract(X).subtract(Y); corner[1] = center.add(X).subtract(Y); corner[2] = center.add(X).add(Y); corner[3] = center.subtract(X).add(Y); computeAxes(); extents.x = w / 2; extents.y = h / 2; computeDimensions(center,angle); } private void computeDimensions(Vector2D center,float angle) { this.center.x = center.x; this.center.y = center.y; this.angle = angle; boundingRect.left = Math.min(Math.min(corner[0].x, corner[3].x), Math.min(corner[1].x, corner[2].x)); boundingRect.top = Math.min(Math.min(corner[0].y, corner[1].y),Math.min(corner[2].y, corner[3].y)); boundingRect.right = Math.max(Math.max(corner[1].x, corner[2].x), Math.max(corner[0].x, corner[3].x)); boundingRect.bottom = Math.max(Math.max(corner[2].y, corner[3].y),Math.max(corner[0].y, corner[1].y)); } public void set(RectF rect) { set(new Vector2D(rect.centerX(),rect.centerY()),rect.width(),rect.height(),0.0f); } // Returns true if other overlaps one dimension of this. private boolean overlaps1Way(OBB2D other) { for (int a = 0; a < axis.length; ++a) { double t = other.corner[0].dot(axis[a]); // Find the extent of box 2 on axis a double tMin = t; double tMax = t; for (int c = 1; c < corner.length; ++c) { t = other.corner[c].dot(axis[a]); if (t < tMin) { tMin = t; } else if (t > tMax) { tMax = t; } } // We have to subtract off the origin // See if [tMin, tMax] intersects [0, 1] if ((tMin > 1 + origin[a]) || (tMax < origin[a])) { // There was no intersection along this dimension; // the boxes cannot possibly overlap. return false; } } // There was no dimension along which there is no intersection. // Therefore the boxes overlap. return true; } //Updates the axes after the corners move. Assumes the //corners actually form a rectangle. private void computeAxes() { axis[0] = corner[1].subtract(corner[0]); axis[1] = corner[3].subtract(corner[0]); // Make the length of each axis 1/edge length so we know any // dot product must be less than 1 to fall within the edge. for (int a = 0; a < axis.length; ++a) { axis[a] = axis[a].divide((axis[a].length() * axis[a].length())); origin[a] = corner[0].dot(axis[a]); } } public void moveTo(Vector2D center) { Vector2D centroid = (corner[0].add(corner[1]).add(corner[2]).add(corner[3])).divide(4.0f); Vector2D translation = center.subtract(centroid); for (int c = 0; c < 4; ++c) { corner[c] = corner[c].add(translation); } computeAxes(); computeDimensions(center,angle); } // Returns true if the intersection of the boxes is non-empty. public boolean overlaps(OBB2D other) { if(right() < other.left()) { return false; } if(bottom() < other.top()) { return false; } if(left() > other.right()) { return false; } if(top() > other.bottom()) { return false; } if(other.getAngle() == 0.0f && getAngle() == 0.0f) { return true; } return overlaps1Way(other) && other.overlaps1Way(this); } public Vector2D getCenter() { return center; } public float getWidth() { return extents.x * 2; } public float getHeight() { return extents.y * 2; } public void setAngle(float angle) { set(center,getWidth(),getHeight(),angle); } public float getAngle() { return angle; } public void setSize(float w,float h) { set(center,w,h,angle); } public float left() { return boundingRect.left; } public float right() { return boundingRect.right; } public float bottom() { return boundingRect.bottom; } public float top() { return boundingRect.top; } public RectF getBoundingRect() { return boundingRect; } public boolean overlaps(float left, float top, float right, float bottom) { if(right() < left) { return false; } if(bottom() < top) { return false; } if(left() > right) { return false; } if(top() > bottom) { return false; } return true; } };

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• 2d tank movement and turret solution

  - by Phil

  Hi! I'm making a simple top-down tank game on the ipad where the user controls the movement of the tank with the left "joystick" and the rotation of the turret with the right one. I've spent several hours just trying to get it to work decently but now I turn to the pros :) I have two referencial objects, one for the movement and one for the rotation. The referencial objects always stay max two units away from the tank and I use them to tell the tank in what direction to move. I chose this approach to decouple movement and rotational behaviour from the raw input of the joysticks, I believe this will make it simpler to implement whatever behaviour I want for the tank. My problem is 1; the turret rotates the long way to the target. With this I mean that the target can be -5 degrees away in rotation and still it rotates 355 degrees instead of -5 degrees. I can't figure out why. The other problem is with the movement. It just doesn't feel right to have the tank turn while moving. I'd like to have a solution that would work as well for the AI as for the player. A blackbox function for the movement where the player only specifies in what direction it should move and it moves there under the constraints that are imposed on it. I am using the standard joystick class found in the Unity iPhone package. This is the code I'm using for the movement: public class TankFollow : MonoBehaviour { //Check angle difference and turn accordingly public GameObject followPoint; public float speed; public float turningSpeed; void Update() { transform.position = Vector3.Slerp(transform.position, followPoint.transform.position, speed * Time.deltaTime); //Calculate angle var forwardA = transform.forward; var forwardB = (followPoint.transform.position - transform.position); var angleA = Mathf.Atan2(forwardA.x, forwardA.z) * Mathf.Rad2Deg; var angleB = Mathf.Atan2(forwardB.x, forwardB.z) * Mathf.Rad2Deg; var angleDiff = Mathf.DeltaAngle(angleA, angleB); //print(angleDiff.ToString()); if (angleDiff > 5) { //Rotate to transform.Rotate(new Vector3(0, (-turningSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); } else if (angleDiff < 5) { transform.Rotate(new Vector3(0, (turningSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); } else { } transform.position = new Vector3(transform.position.x, 0, transform.position.z); } } And this is the code I'm using to rotate the turret: void LookAt() { var forwardA = -transform.right; var forwardB = (toLookAt.transform.position - transform.position); var angleA = Mathf.Atan2(forwardA.x, forwardA.z) * Mathf.Rad2Deg; var angleB = Mathf.Atan2(forwardB.x, forwardB.z) * Mathf.Rad2Deg; var angleDiff = Mathf.DeltaAngle(angleA, angleB); //print(angleDiff.ToString()); if (angleDiff - 180 > 1) { //Rotate to transform.Rotate(new Vector3(0, (turretSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); } else if (angleDiff - 180 < -1) { transform.Rotate(new Vector3(0, (-turretSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); print((angleDiff - 180).ToString()); } else { } } Since I want the turret reference point to turn in relation to the tank (when you rotate the body, the turret should follow and not stay locked on since it makes it impossible to control when you've got two thumbs to work with), I've made the TurretFollowPoint a child of the Turret object, which in turn is a child of the body. I'm thinking that I'm making it too difficult for myself with the reference points but I'm imagining that it's a good idea. Please be honest about this point. So I'll be grateful for any help I can get! I'm using Unity3d iPhone. Thanks!

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• How to Draw texture between 2 Vector3

  - by Sparky41

  My scenario: RTS combat style, 1 unit fires beam on another unit My problem is i want to draw a flat texture between 2 Vector3 points. I have looked at various Billboarding styles but that doesn't give me a proper solution. I looked at this: http://msdn.microsoft.com/en-us/library/bb464051.aspx is BasicEffect and DrawPrimitives the correct solution just stretch the texture to the distance between point of origin to target? I used the quad class they used but i found this it seemed to inflexible So my question to you is how would i go about this sort of problem? Regards

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• If Expression True in Immediate Window But Code In if Block Never Runs

  - by Julian

  I set a break point in my code in MonoDevelop to break whenever I click on a surface. I then enter the immediate window and test to see if the the if statement will return true in comparing two Vector3's. It does return true. However, when I step over, the code is never run as though the statement evaluated false. Does anyone know how this could be possible? I've attached a screenshot. Here is the picture of my debug window and immediate window. You can see where the immediate window evaluates to true. The second breakpoint is not hit. Here are the details of the two Vector3's I am comparing. Does anyone know why I am experiencing this? It really seems like an anomaly to me :/ Does it have something to do with threading?

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• Transform 3D vectors between coordinate systems

  - by Nir Cig

  I've got 6 points in 3D space: A,B,C,D,E,F, that represent 4 vectors. AB is perpendicular to AC and DE is perpendicular to DF. I need to find a transformation matrix M, that transforms AB to DE and AC to DF. In other words: M·AB=DE, M·AC=DF If no scaling was involved, this could be solved with a simple rotation matrix. But since the ratios |AB|/|DE|, |AC|/|DF| might be different, I'm not sure how to proceed.

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• How to make an object stay relative to another object

  - by Nick

  In the following example there is a guy and a boat. They have both a position, orientation and velocity. The guy is standing on the shore and would like to board. He changes his position so he is now standing on the boat. The boat changes velocity and orientation and heads off. My character however has a velocity of 0,0,0 but I would like him to stay onboard. When I move my character around, I would like to move as if the boat was the ground I was standing on. How do keep my character aligned properly with the boat? It is exactly like in World Of Warcraft, when you board a boat or zeppelin. This is my physics code for the guy and boat: this.velocity.addSelf(acceleration.multiplyScalar(dTime)); this.position.addSelf(this.velocity.clone().multiplyScalar(dTime)); The guy already has a reference to the boat he's standing on, and thus knows the boat's position, velocity, orientation (even matrices or quaternions can be used).

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• OpenGL not rendering my images to the screen

  - by Brendan Webster

  for some reason my game isn't showing the image I am rendering to the screen. My engine is state based, and at the beginning I set the logo, but it isn't showing on the screen. Here is my method of doing so first I create one image and assign some values to it's preset values. //create one image instance for the logo background O_File.v_Create_Images(1); //set the atributes of the background //first Image O_File.sImage[0].nImageDepth = -30.0f; O_File.sImage[0].sImageLocation = "image.bmp"; //load the images int O_File.v_Load_Images(); Then I load them with DevIL void C_File_Manager::v_Load_Images() { ilGenImages(1, &image); ilBindImage(image); for(int i = 0;i < sImage.size();i++) { success = ilLoadImage(sImage[i].sImageLocation.c_str()); if (success) { success = ilConvertImage(IL_RGBA, IL_UNSIGNED_BYTE); glGenTextures(1, &image); glBindTexture(GL_TEXTURE_2D, image); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR); glTexImage2D(GL_TEXTURE_2D, 0, 4, ilGetInteger(IL_IMAGE_WIDTH), ilGetInteger(IL_IMAGE_HEIGHT), 0, ilGetInteger(IL_IMAGE_FORMAT), GL_UNSIGNED_BYTE, ilGetData()); //asign values to the width and height of the image if they are already not assigned if(sImage[i].nImageHeight == 0) sImage[i].nImageHeight = ilGetInteger(IL_IMAGE_HEIGHT); if(sImage[i].nImageWidth == 0) sImage[i].nImageWidth = ilGetInteger(IL_IMAGE_WIDTH); std::cout << sImage[i].nImageHeight << std::endl; const std::string word = sImage[i].sImageLocation.c_str(); std::cout << sImage[i].sImageLocation.c_str() << std::endl; ilLoadImage(word.c_str()); ilDeleteImages(1, &image); } } } and then I apply them to the screen void C_File_Manager::v_Apply_Images() { glMatrixMode(GL_MODELVIEW); glLoadIdentity(); for(int i = 0;i < sImage.size();i++) { //move the image to where it should be on the screen; glTranslatef(sImage[i].nImageX,sImage[i].nImageY,sImage[i].nImageDepth); //rotate image around the 3 axes glRotatef(sImage[i].fImageAngleX,1,0,0); glRotatef(sImage[i].fImageAngleY,0,1,0); glRotatef(sImage[i].fImageAngleZ,0,0,1); //scale the image glScalef(1,1,1); //center the image glTranslatef((sImage[i].nImageWidth/2),(sImage[i].nImageHeight/2),0); //draw the box that will encase the loaded image glBegin(GL_QUADS); //change the color of the loaded image; glColor4f(1,1,1,1); //top left corner of image glNormal3f(0.0,0,0.0); glTexCoord2f (1.0, 0.0); glVertex3f(0,0,sImage[i].nImageDepth); //top right corner of image glNormal3f(1.0,0,0.0); glTexCoord2f (1.0, 1.0); glVertex3f(0,sImage[i].nImageHeight,sImage[i].nImageDepth); //bottom right corner of image glNormal3f(-1.0,0,0.0); glTexCoord2f (0.0, 1.0); glVertex3f(sImage[i].nImageWidth,sImage[i].nImageHeight,sImage[i].nImageDepth); //bottom left corner of image glNormal3f(-1.0,0,0.0); glTexCoord2f(0.0, 0.0); glVertex3f(sImage[i].nImageWidth,0,sImage[i].nImageDepth); glEnd(); } } when I debug there is no errors at all, but yet the images don't show up on the screen, I have positioned the camera at (0,0,-1) and that is where the images should show up. the clipping plane is set 1 to 1000. There is probably some random problem with the code, but I just can't catch it.

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• Split a 2D scene in layers or have a z coordinate

  - by Bane

  I am in the process of writing a 2D game engine, and a dilemma emerged. Let me explain the situation... I have a Scene class, to which various objects can be added (Drawable, ParticleEmitter, Light2D, etc), and as this is a 2D scene, things will obviously be drawn over each other. My first thought was that I could have basic add and remove methods, but I soon realized that then there would be no way for the programmer to control the order in which things were drawn. So I can up with two options, each with its pros and cons. A) Would be to split the scene in layers. By that I mean instead of having the scene be a container of objects, have it be a container of layers, which are in turn the containers of objects. B) Would require to have some kind of z-coordinate, and then have the scene sorted so objects with lower z get drawn first. Option A is pretty solid, but the problem is with the lights. In what layer do I add it? Does it work cross-layer? On all bottom layers? And I still need the Z coordinate to calculate the shadow! Option B would require me to change all my code from having Vector2D positions, to some kind of class that inherits from Vector2D and adds a z coordinate to it (I don't want it to be a Vector3D because I still need all the same methods the 2D kind has, just with .z clamped on). Am I missing something? Is there an alternative to these methods? I'm working in Javascript, if that makes a difference.

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• Moving in a diamond - enemy gets stuck

  - by Fibericon

  I have an enemy that I would like to move as follows: Start at (0, 200, 0) Move to (200, 0, 0) Move to (0, -200, 0) Move to (-200, 0, 0) Move to start point, repeat as long as it remains active. This is what I've done to achieve that: if (position.X < 200 && position.Y > 0) { Velocity = new Vector3(1, -1, 0) * speed; } else if (position.X >= 200 && position.Y <= 0 && position.Y > -200) { Velocity = new Vector3(-1, -1, 0) * speed; } else if (position.X <= 0 && position.Y <= -200) { Velocity = new Vector3(-1, 1, 0) * speed; } else { Velocity = new Vector3(1, 1, 0) * speed; } It moves to the second point, but then gets stuck and appears to vibrate in place. How should I be doing this?

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• How can I calculate a vertex normal for a hard edge?

  - by K.G.

  Here is a picture of a lovely polygon: Circled is a vertex, and numbered are its adjacent faces. I have calculated the normals of those faces as such (not yet normalized, 0-indexed): Vertex 1 normal 0: 0.000000 0.000000 -0.250000 Vertex 1 normal 1: 0.000000 0.000000 -0.250000 Vertex 1 normal 2: -0.250000 0.000000 0.000000 Vertex 1 normal 3: -0.250000 0.000000 0.000000 Vertex 1 normal 4: 0.250000 0.000000 0.000000 What I'm wondering is, how can I determine, taken as given that I want this vertex to represent a hard edge, whether its normal should be the normal of 1/2 or 3/4? My plan after I glanced at the sketch I used to put this together was "Ha! I'll just use whichever two faces have the same normal!" and now I see that there are two sets of two faces for which this is true. Is there a rule I can apply based on the face winding, angle of the adjacent edges, moon phase, coin flip, to consistently choose a normal direction for this box? For the record, all of the other polygons I plan to use will have their normals dictated in Maya, but after encountering this problem, it made me really curious.

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• Weird rotation problem

  - by Phil

  I'm creating a simple tank game. No matter what I do, the turret keeps facing the target with it's side. I just can't figure out how to turn it 90 degrees in Y once so it faces it correctly. I've checked the pivot in Maya and it doesn't matter how I change it. This is the code I use to calculate how to face the target: void LookAt() { var forwardA = transform.forward; var forwardB = (toLookAt.transform.position - transform.position); var angleA = Mathf.Atan2(forwardA.x, forwardA.z) * Mathf.Rad2Deg; var angleB = Mathf.Atan2(forwardB.x, forwardB.z) * Mathf.Rad2Deg; var angleDiff = Mathf.DeltaAngle(angleA, angleB); //print(angleDiff.ToString()); if (angleDiff > 20) { //Rotate to transform.Rotate(new Vector3(0, (-turretSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); } else if (angleDiff < 20) { transform.Rotate(new Vector3(0, (turretSpeed * Time.deltaTime),0)); //transform.rotation = new Quaternion(transform.rotation.x, transform.rotation.y + adjustment, transform.rotation.z, transform.rotation.w); } else { } } I'm using Unity3d and would appreciate any help I can get! Thanks!

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• Relative cam movement and momentum on arbitrary surface

  - by user29244

  I have been working on a game for quite long, think sonic classic physics in 3D or tony hawk psx, with unity3D. However I'm stuck at the most fundamental aspect of movement. The requirement is that I need to move the character in mario 64 fashion (or sonic adventure) aka relative cam input: the camera's forward direction always point input forward the screen, left or right input point toward left or right of the screen. when input are resting, the camera direction is independent from the character direction and the camera can orbit the character when input are pressed the character rotate itself until his direction align with the direction the input is pointing at. It's super easy to do as long your movement are parallel to the global horizontal (or any world axis). However when you try to do this on arbitrary surface (think moving along complex curved surface) with the character sticking to the surface normal (basically moving on wall and ceiling freely), it seems harder. What I want is to achieve the same finesse of movement than in mario but on arbitrary angled surfaces. There is more problem (jumping and transitioning back to the real world alignment and then back on a surface while keeping momentum) but so far I didn't even take off the basics. So far I have accomplish moving along the curved surface and the relative cam input, but for some reason direction fail all the time (point number 3, the character align slowly to the input direction). Do you have an idea how to achieve that? Here is the code and some demo so far: The demo: https://dl.dropbox.com/u/24530447/flash%20build/litesonicengine/LiteSonicEngine5.html Camera code: using UnityEngine; using System.Collections; public class CameraDrive : MonoBehaviour { public GameObject targetObject; public Transform camPivot, camTarget, camRoot, relcamdirDebug; float rot = 0; //---------------------------------------------------------------------------------------------------------- void Start() { this.transform.position = targetObject.transform.position; this.transform.rotation = targetObject.transform.rotation; } void FixedUpdate() { //the pivot system camRoot.position = targetObject.transform.position; //input on pivot orientation rot = 0; float mouse_x = Input.GetAxisRaw( "camera_analog_X" ); // rot = rot + ( 0.1f * Time.deltaTime * mouse_x ); // wrapAngle( rot ); // //when the target object rotate, it rotate too, this should not happen UpdateOrientation(this.transform.forward,targetObject.transform.up); camRoot.transform.RotateAround(camRoot.transform.up,rot); //debug the relcam dir RelativeCamDirection() ; //this camera this.transform.position = camPivot.position; //set the camera to the pivot this.transform.LookAt( camTarget.position ); // } //---------------------------------------------------------------------------------------------------------- public float wrapAngle ( float Degree ) { while (Degree < 0.0f) { Degree = Degree + 360.0f; } while (Degree >= 360.0f) { Degree = Degree - 360.0f; } return Degree; } private void UpdateOrientation( Vector3 forward_vector, Vector3 ground_normal ) { Vector3 projected_forward_to_normal_surface = forward_vector - ( Vector3.Dot( forward_vector, ground_normal ) ) * ground_normal; camRoot.transform.rotation = Quaternion.LookRotation( projected_forward_to_normal_surface, ground_normal ); } float GetOffsetAngle( float targetAngle, float DestAngle ) { return ((targetAngle - DestAngle + 180)% 360) - 180; } //---------------------------------------------------------------------------------------------------------- void OnDrawGizmos() { Gizmos.DrawCube( camPivot.transform.position, new Vector3(1,1,1) ); Gizmos.DrawCube( camTarget.transform.position, new Vector3(1,5,1) ); Gizmos.DrawCube( camRoot.transform.position, new Vector3(1,1,1) ); } void OnGUI() { GUI.Label(new Rect(0,80,1000,20*10), "targetObject.transform.up : " + targetObject.transform.up.ToString()); GUI.Label(new Rect(0,100,1000,20*10), "target euler : " + targetObject.transform.eulerAngles.y.ToString()); GUI.Label(new Rect(0,100,1000,20*10), "rot : " + rot.ToString()); } //---------------------------------------------------------------------------------------------------------- void RelativeCamDirection() { float input_vertical_movement = Input.GetAxisRaw( "Vertical" ), input_horizontal_movement = Input.GetAxisRaw( "Horizontal" ); Vector3 relative_forward = Vector3.forward, relative_right = Vector3.right, relative_direction = ( relative_forward * input_vertical_movement ) + ( relative_right * input_horizontal_movement ) ; MovementController MC = targetObject.GetComponent<MovementController>(); MC.motion = relative_direction.normalized * MC.acceleration * Time.fixedDeltaTime; MC.motion = this.transform.TransformDirection( MC.motion ); //MC.transform.Rotate(Vector3.up, input_horizontal_movement * 10f * Time.fixedDeltaTime); } } Mouvement code: using UnityEngine; using System.Collections; public class MovementController : MonoBehaviour { public float deadZoneValue = 0.1f, angle, acceleration = 50.0f; public Vector3 motion ; //-------------------------------------------------------------------------------------------- void OnGUI() { GUILayout.Label( "transform.rotation : " + transform.rotation ); GUILayout.Label( "transform.position : " + transform.position ); GUILayout.Label( "angle : " + angle ); } void FixedUpdate () { Ray ground_check_ray = new Ray( gameObject.transform.position, -gameObject.transform.up ); RaycastHit raycast_result; Rigidbody rigid_body = gameObject.rigidbody; if ( Physics.Raycast( ground_check_ray, out raycast_result ) ) { Vector3 next_position; //UpdateOrientation( gameObject.transform.forward, raycast_result.normal ); UpdateOrientation( gameObject.transform.forward, raycast_result.normal ); next_position = GetNextPosition( raycast_result.point ); rigid_body.MovePosition( next_position ); } } //-------------------------------------------------------------------------------------------- private void UpdateOrientation( Vector3 forward_vector, Vector3 ground_normal ) { Vector3 projected_forward_to_normal_surface = forward_vector - ( Vector3.Dot( forward_vector, ground_normal ) ) * ground_normal; transform.rotation = Quaternion.LookRotation( projected_forward_to_normal_surface, ground_normal ); } private Vector3 GetNextPosition( Vector3 current_ground_position ) { Vector3 next_position; // //-------------------------------------------------------------------- // angle = 0; // Vector3 dir = this.transform.InverseTransformDirection(motion); // angle = Vector3.Angle(Vector3.forward, dir);// * 1f * Time.fixedDeltaTime; // // if(angle > 0) this.transform.Rotate(0,angle,0); // //-------------------------------------------------------------------- next_position = current_ground_position + gameObject.transform.up * 0.5f + motion ; return next_position; } } Some observation: I have the correct input, I have the correct translation in the camera direction ... but whenever I attempt to slowly lerp the direction of the character in direction of the input, all I get is wild spin! Sad Also discovered that strafing to the right (immediately at the beginning without moving forward) has major singularity trapping on the equator!! I'm totally lost and crush (I have already done a much more featured version which fail at the same aspect)

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• 3D rotation matrices deform object while rotating

  - by Kevin

  I'm writing a small 3D renderer (using an orthographic projection right now). I've run into some trouble with my 3D rotation matrices. They seem to squeeze my 3D object (a box primitive) at certain angles. Here's a live demo (only tested in Google Chrome): http://dl.dropbox.com/u/109400107/3D/index.html The box is viewed from the top along the Y axis and is rotating around the X and Z axis. These are my 3 rotation matrices (Only rX and rZ are being used): var rX = new Matrix([ [1, 0, 0], [0, Math.cos(radiants), -Math.sin(radiants)], [0, Math.sin(radiants), Math.cos(radiants)] ]); var rY = new Matrix([ [Math.cos(radiants), 0, Math.sin(radiants)], [0, 1, 0], [-Math.sin(radiants), 0, Math.cos(radiants)] ]); var rZ = new Matrix([ [Math.cos(radiants), -Math.sin(radiants), 0], [Math.sin(radiants), Math.cos(radiants), 0], [0, 0, 1] ]); Before projecting the verticies I multiply them by rZ and rX like so: vert1.multiply(rZ); vert1.multiply(rX); vert2.multiply(rZ); vert2.multiply(rX); vert3.multiply(rZ); vert3.multiply(rX); The projection itself looks like this: bX = (pos.x + (vert1.x*scale)); bY = (pos.y + (vert1.z*scale)); Where "pos.x" and "pos.y" is an offset for centering the box on the screen. I just can't seem to find a solution to this and I'm still relativly new to working with Matricies. You can view the source-code of the demo page if you want to see the whole thing.

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• Adding 'swerve' to a direction

  - by Skoder

  Hey. I'm not much of a maths expert, so this is probably quite straight forward. I was playing a soccer flash game where you take free kicks. You provide Power, Swerve and Direction. I'm reading up on vectors and such so I can use the direction and power information to shoot the ball with the correct velocity. What I don't understand is how the 'Swerve' information is used. What formula connects the Swerve information with the Direction and Power? (This is all in 2D) Thanks for any advice.

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• Moving objects colliding when using unalligned collision avoidance (steering)

  - by James Bedford

  I'm having trouble with unaligned collision avoidance for what I think is a rare case. I have set two objects to move towards each other but with a slight offset, so one of the objects is moving slightly upwards, and one of the objects is moving slightly downwards. In my unaligned collision avoidance steering algorithm I'm finding the points on the object's forward line and the other object's forward line where these two lines are the closest. If these closest points are within a collision avoidance distance, and if the distance between them is smaller than the two radii of the two object's bounding spheres, then the objects should steer away in the appropriate direction. The problem is that for my case, the closest points on the lines are calculated to be really far away from the actual collision point. This is because the two forward lines for each object are moving away from each other as the objects pass. The problem is that because of this, no steering takes place, and the two objects partially collide. Does anyone have any suggestions as to how I can correctly calculate the point of collision? Perhaps by somehow taking into account the size of the two objects?

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• How do I find the closest points(thereby forming a polygon) enclosing a particular point?(see image)

  - by nilspin

  I am working with a game engine, and my task is to add code for simulating fracture of rigid meshes. Right now I'm only working on breaking a cube. I am using Voronoi's algorithm to make a (realistic)fractured shard and I am using the half-plane method to generate a voronoi cell. Now the way I do this is for every seed point, I make planes that are perpendicular bisector planes(the straight black lines in the image) with rest of the seed points and I calculate the intersections of all these planes to give me distinct points(all the orange dots). I've gotten this far. Out of all these calculated intersection points, I only need the ones that are closest and enclosing the seed point(the points encircled in red) and I need to discard all the rest. Information that I have : 1) Plane equations of all planes(defined by normalized normal vectors and their distance from origin) 2) Points of intersection(that I've calculated) Can anybody help me find out how I can find the points encircled in red? Thanks.

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• Detect if square in grid is within a diamond shape

  - by myrkos

  So I have a game in which basically everything is a square inside a big grid. It's easy to check if a square is inside a box whose center is another square: *** x *o* --> x is not in o's square *** **x *o* --> x IS in o's square *** This can be done by simply subtracting the coordinates of o and x, then taking the largest coordinate of that and comparing it with the half side length. Now I want to do the same thing but check if x is in o's diamond, like so: * **x **o** --> x IS in o's diamond *** * What would be the best way to check if a square is in another square's surrounding diamond-shaped area, given the diamond's half width/height?

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• Interpolation between two 3D points?

  - by meds

  I'm working with some splines which define a path a character follows (you can see a gameplay video here to get a better understanding of what's going on: http://www.youtube.com/watch?v=BndobjOiZ6g). Basically the characters 'forward' look direction is set to the 'forward' direction of the spline and when players tilt their phone left and right the character is strafed along its 'right' coordinate. The issue with this is (rather obviously) in performance, interpolating over a spline to find the nearest position and tangent relative to the player is an incredibly costly operation. To get by this I cache a finite number of positions in what I call 'SplineDetails', the class is as follows: public class SplineDetails { public SplineDetails() { Forward = Vector3.forward; Position = Vector3.one * float.MaxValue; Alpha = -1; } public float Alpha; // [0,1] measured along length of spline where 0 is the initial point and 1 is the end point of the spline public Vector3 Position; // the point of the spline at this alpha public Vector3 Forward; // the forward tangent of the spline at this alpha } I populate this with say 30 coordinates and I can give a rough estimate of a coordinate and 'forward' based on a position past in. It's not as accurate but it's much faster. But now I'd like to make the system work better by estimating positions and 'forward' directions by interpolating between two of the cached points though I'm stuck trying to figure out some logic. My first problem is, how can I determine between which two points the object is? Given each point can be placed at different intervals along the spline it could mean that two points in front or behind the object can be closer to the object. The other problem is to figure out the proportion between the two paths it's between, i.e. if there is a point a at coordinate (0,0,0) and point b at coordinate (1,0,0) if the object is at position (0.5,0,0) then the result it should give is '0.5' (as it is equal distance away from point a and point b). That's a simple example, but what if the object is at coordinate (0.5,3,0) for example?

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• Calculating the rotational force of a 2D sprite

  - by Jon

  I am wondering if someone has an elegant way of calculating the following scenario. I have an object of (n) number of squares, random shapes, but we will pretend they are all rectangles. We are dealing with no gravity, so consider the object in space, from a top down perspective. I am applying a force to the object at a specific square (as illustrated below). How do I calculate the rotational angle, based on the force being applied, at the location being applied. If applied in the center square, it would go straight. How should it behave the further I move from the center? How do I calculate the rotational velocity?

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• Need the co-ordinates of innerPolygon

  - by user960567

  Let say I have this diagram, Given that i have all the co-ordinates of outer polygon and the distance between inner and outer polygon is d is also given. How to calculate the inner polygon co-ordinates? Edit: I was able to solved the issue by getting the mid-points of all lines. From these mid-points I can move d distance, So I can get three points. No I have 3 points and 3 slopes. From this, I can get three new equations. Simultaneously, solving the equation get the 3 points.

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• What is going on in this SAT/vector projection code?

  - by ssb

  I'm looking at the example XNA SAT collision code presented here: http://www.xnadevelopment.com/tutorials/rotatedrectanglecollisions/rotatedrectanglecollisions.shtml See the following code: private int GenerateScalar(Vector2 theRectangleCorner, Vector2 theAxis) { //Using the formula for Vector projection. Take the corner being passed in //and project it onto the given Axis float aNumerator = (theRectangleCorner.X * theAxis.X) + (theRectangleCorner.Y * theAxis.Y); float aDenominator = (theAxis.X * theAxis.X) + (theAxis.Y * theAxis.Y); float aDivisionResult = aNumerator / aDenominator; Vector2 aCornerProjected = new Vector2(aDivisionResult * theAxis.X, aDivisionResult * theAxis.Y); //Now that we have our projected Vector, calculate a scalar of that projection //that can be used to more easily do comparisons float aScalar = (theAxis.X * aCornerProjected.X) + (theAxis.Y * aCornerProjected.Y); return (int)aScalar; } I think the problems I'm having with this come mostly from translating physics concepts into data structures. For example, earlier in the code there is a calculation of the axes to be used, and these are stored as Vector2, and they are found by subtracting one point from another, however these points are also stored as Vector2s. So are the axes being stored as slopes in a single Vector2? Next, what exactly does the Vector2 produced by the vector projection code represent? That is, I know it represents the projected vector, but as it pertains to a Vector2, what does this represent? A point on a line? Finally, what does the scalar at the end actually represent? It's fine to tell me that you're getting a scalar value of the projected vector, but none of the information I can find online seems to tell me about a scalar of a vector as it's used in this context. I don't see angles or magnitudes with these vectors so I'm a little disoriented when it comes to thinking in terms of physics. If this final scalar calculation is just a dot product, how is that directly applicable to SAT from here on? Is this what I use to calculate maximum/minimum values for overlap? I guess I'm just having trouble figuring out exactly what the dot product is representing in this particular context. Clearly I'm not quite up to date on my elementary physics, but any explanations would be greatly appreciated.

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• Converting Degrees to X and Y Coordinate change

  - by gopgop

  I am using a float positioning system in my game. IE float x,y,z now I want to get the location of the mouse, then to fire an arrow to it. X0 = the players X location X1 = the mouse X location Y0 = the players Y location Y1 = the mouse Y location I want to make a method that the parameters are Degrees and it sets my Yspeed and my Xspeed accordingly to get to the mouse xy starting at player xy How do would I accomplish this?

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• Swapping axis labels between 2D and 3D coordinates

  - by Will

  My game world is 3D. The map is only 2D, however. It is natural to think of the map as having an X and Y axis. And it is natural to think of the world has having an X, Y and Z axis, where Y is upwards. That is to say, X Y in 2D map coordinates is X Z in 3D coordinates. What conventions and approaches do you have to keeping things straight at a code level to make mapping between them natural? (Is Y usually upwards in 3D? Or do you have X and Z in map coordinates, or?)

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