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• Robust line of sight test on the inside of a polygon with tolerance

  - by David Gouveia

  Foreword This is a followup to this question and the main problem I'm trying to solve. My current solution is an hack which involves inflating the polygon, and doing most calculations on the inflated polygon instead. My goal is to remove this step completely, and correctly solve the problem with calculations only. Problem Given a concave polygon and treating all of its edges as if they were walls in a level, determine whether two points A and B are in line of sight of each other, while accounting for some degree of floating point errors. I'm currently basing my solution on a series of line-segment interection tests. In other words: If any of the end points are outside the polygon, they are not in line of sight. If both end points are inside the polygon, and the line segment from A to B crosses any of the edges from the polygon, then they are not in line of sight. If both end points are inside the polygon, and the line segment from A to B does not cross any of the edges from the polygon, then they are in line of sight. But the problem is dealing correctly with all the edge cases. In particular, it must be able to deal with all the situations depicted below, where red lines are examples that should be rejected, and green lines are examples that should be accepted. I probably missed a few other situations, such as when the line segment from A to B is colinear with an edge, but one of the end points is outside the polygon. One point of particular interest is the difference between 1 and 9. In both cases, both end points are vertices of the polygon, and there are no edges being intersected, but 1 should be rejected while 9 should be accepted. How to distinguish these two? I could check some middle point within the segment to see if it falls inside or not, but it's easy to come up with situations in which it would fail. Point 7 was also pretty tricky and I had to to treat it as a special case, which checks if two points are adjacent vertices of the polygon directly. But there are also other chances of line segments being col linear with the edges of the polygon, and I'm still not entirely sure how I should handle those cases. Is there any well known solution to this problem?

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• Transforming a primitive tetrahedron into a primitive icosahedron?

  - by Djentleman

  I've created a tetrahedron by creating a BoundingBox and building the faces of the tetrahedron within the bounding box as follows (see image as well): VertexPositionNormalTexture[] vertices = new VertexPositionNormalTexture[12]; BoundingBox box = new BoundingBox(new Vector3(-1f, 1f, 1f), new Vector3(1f, -1f, -1f)); vertices[0].Position = box.GetCorners()[0]; vertices[1].Position = box.GetCorners()[2]; vertices[2].Position = box.GetCorners()[7]; vertices[3].Position = box.GetCorners()[0]; vertices[4].Position = box.GetCorners()[5]; vertices[5].Position = box.GetCorners()[2]; vertices[6].Position = box.GetCorners()[5]; vertices[7].Position = box.GetCorners()[7]; vertices[8].Position = box.GetCorners()[2]; vertices[9].Position = box.GetCorners()[5]; vertices[10].Position = box.GetCorners()[0]; vertices[11].Position = box.GetCorners()[7]; What would I then have to do to transform this tetrahedron into an icosahedron? Similar to this image: I understand the concept but applying it is another thing entirely for me.

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• Convex Hull for Concave Objects

  - by Lighthink

  I want to implement GJK and I want it to handle concave shapes too (almost all my shapes are concave). I've thought of decomposing the concave shape into convex shapes and then building a hierarchical tree out of convex shapes, but I do not know how to do it. Nothing I could find on the Internet about it wasn't satisfying my needs, so maybe someone can point me in the right direction or give a full explanation.

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• simple collision detection

  - by Rob

  Imagine 2 squares sitting side by side, both level with the ground: http://img19.imageshack.us/img19/8085/sqaures2.jpg A simple way to detect if one is hitting the other is to compare the location of each side. They are touching if ALL of the following are NOT true: The right square's left side is to the right of the left square's right side. The right square's right side is to the left of the left square's left side. The right square's bottom side is above the left square's top side. The right square's top side is below the left square's bottom side. If any of those are true, the squares are not touching. If all of those are false, the squares are touching. But consider a case like this, where one square is at a 45 degree angle: http://img189.imageshack.us/img189/4236/squaresb.jpg Is there an equally simple way to determine if those squares are touching?

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• Intersection points of plane set forming convex hull

  - by Toji

  Mostly looking for a nudge in the right direction here. Given a set of planes (defined as a normal and distance from origin) that form a convex hull, I would like to find the intersection points that form the corners of that hull. More directly, I'm looking for a way to generate a point cloud appropriate to provide to Bullet. Bonus points if someone knows of a way I could give bullet the plane list directly, since I somewhat suspect that's what it's building on the backend anyway.

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• Circle-Line Collision Detection Problem

  - by jazzdawg

  I am currently developing a breakout clone and I have hit a roadblock in getting collision detection between a ball (circle) and a brick (convex polygon) working correctly. I am using a Circle-Line collision detection test where each line represents and edge on the convex polygon brick. For the majority of the time the Circle-Line test works properly and the points of collision are resolved correctly. Collision detection working correctly. However, occasionally my collision detection code returns false due to a negative discriminant when the ball is actually intersecting the brick. Collision detection failing. I am aware of the inefficiency with this method and I am using axis aligned bounding boxes to cut down on the number of bricks tested. My main concern is if there are any mathematical bugs in my code below. /* * from and to are points at the start and end of the convex polygons edge. * This function is called for every edge in the convex polygon until a * collision is detected. */ bool circleLineCollision(Vec2f from, Vec2f to) { Vec2f lFrom, lTo, lLine; Vec2f line, normal; Vec2f intersectPt1, intersectPt2; float a, b, c, disc, sqrt_disc, u, v, nn, vn; bool one = false, two = false; // set line vectors lFrom = from - ball.circle.centre; // localised lTo = to - ball.circle.centre; // localised lLine = lFrom - lTo; // localised line = from - to; // calculate a, b & c values a = lLine.dot(lLine); b = 2 * (lLine.dot(lFrom)); c = (lFrom.dot(lFrom)) - (ball.circle.radius * ball.circle.radius); // discriminant disc = (b * b) - (4 * a * c); if (disc < 0.0f) { // no intersections return false; } else if (disc == 0.0f) { // one intersection u = -b / (2 * a); intersectPt1 = from + (lLine.scale(u)); one = pointOnLine(intersectPt1, from, to); if (!one) return false; return true; } else { // two intersections sqrt_disc = sqrt(disc); u = (-b + sqrt_disc) / (2 * a); v = (-b - sqrt_disc) / (2 * a); intersectPt1 = from + (lLine.scale(u)); intersectPt2 = from + (lLine.scale(v)); one = pointOnLine(intersectPt1, from, to); two = pointOnLine(intersectPt2, from, to); if (!one && !two) return false; return true; } } bool pointOnLine(Vec2f p, Vec2f from, Vec2f to) { if (p.x >= min(from.x, to.x) && p.x <= max(from.x, to.x) && p.y >= min(from.y, to.y) && p.y <= max(from.y, to.y)) return true; return false; }

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• "Walking" along a rotating surface in LimeJS

  - by Dave Lancea

  I'm trying to have a character walk along a plank (a long, thin rectangle) that works like a seesaw, being rotated around a central point by box2d physics (falling objects). I want the left and right arrow keys to move the player up and down the plank, regardless of it's slope, and I don't want to use real physics for the player movement. My idea for achieving this was to compute the coordinate based on the rotation of the plank and the current location "up" or "down" the board. My math is derived from here: http://math.stackexchange.com/questions/143932/calculate-point-given-x-y-angle-and-distance Here's the code I have so far: movement = 0; if(keys[37]){ // Left movement = -3; } if(keys[39]){ // Right movement = 3; } // this.plank is a LimeJS sprite. // getRotation() Should return an angle in degrees var rotation = this.plank.getRotation(); // this.current_plank_location is initialized as 0 this.current_plank_location += movement; var x_difference = this.current_plank_location * Math.cos(rotation); var y_difference = this.current_plank_location * Math.sin(rotation); this.setPosition(seesaw.PLANK_CENTER_X + x_difference, seesaw.PLANK_CENTER_Y + y_difference); This code causes the player to swing around in a circle when they are out of the center of the plank given a slight change in rotation of the plank. Any ideas on how I can get the player position to follow the board position?

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• Wrong faces culled in OpenGL when drawing a rectangular prism

  - by BadSniper

  I'm trying to learn opengl. I did some code for building a rectangular prism. I don't want to draw back faces so I used glCullFace(GL_BACK), glEnable(GL_CULL_FACE);. But I keep getting back faces also when viewing from front and also sometimes when rotating sides are vanishing. Can someone point me in right direction? glPolygonMode(GL_FRONT,GL_LINE); // draw wireframe polygons glColor3f(0,1,0); // set color green glCullFace(GL_BACK); // don't draw back faces glEnable(GL_CULL_FACE); // don't draw back faces glTranslatef(-10, 1, 0); // position glBegin(GL_QUADS); // face 1 glVertex3f(0,-1,0); glVertex3f(0,-1,2); glVertex3f(2,-1,2); glVertex3f(2,-1,0); // face 2 glVertex3f(2,-1,2); glVertex3f(2,-1,0); glVertex3f(2,5,0); glVertex3f(2,5,2); // face 3 glVertex3f(0,5,0); glVertex3f(0,5,2); glVertex3f(2,5,2); glVertex3f(2,5,0); // face 4 glVertex3f(0,-1,2); glVertex3f(2,-1,2); glVertex3f(2,5,2); glVertex3f(0,5,2); // face 5 glVertex3f(0,-1,2); glVertex3f(0,-1,0); glVertex3f(0,5,0); glVertex3f(0,5,2); // face 6 glVertex3f(0,-1,0); glVertex3f(2,-1,0); glVertex3f(2,5,0); glVertex3f(0,5,0); glEnd();

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• Algorithm to calculate trajectories from vector field

  - by cheeesus

  I have a two-dimensional vector field, i.e., for each point (x, y) I have a vector (u, v), whereas u and v are functions of x and y. This vector field canonically defines a set of trajectories, i.e. a set of paths a particle would take if it follows along the vector field. In the following image, the vector field is depicted in red, and there are four trajectories which are partly visible, depicted in dark red: I need an algorithm which efficiently calculates some trajectories for a given vector field. The trajectories must satisfy some kind of minimum denseness in the plane (for every point in the plane we must have a 'nearby' trajectory), or some other condition to get a reasonable set of trajectories. I could not find anything useful on Google on this, and Stackexchange doesn't seem to handle the topic either. Before I start devising such an algorithm by myself: Are there any known algorithms for this problem? What is their name, for which keywords do I have to search?

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• Adding tolerance to a point in polygon test

  - by David Gouveia

  I've been using this method which was taken from Game Coding Complete to detect whether a point is inside of a polygon. It works in almost every case, but is failing on a few edge cases, and I can't figure out the reason. For example, given a polygon with vertices at (0,0) (0,100) and (100,100), the algorithm is returning: True for any point strictly inside the polygon False for any of the vertices False for (0, 50) which lies on one of the edges of the polygon True (?) for (50,50) which is also on one of the edges of the polygon I'd actually like to relax the algorithm so that it returns true in all of these cases. In other words, it should return true for points that are strictly inside, for the vertices themselves, and for points on the edges of the polygon. If possible I'd also like to give it enough tolerance so that it always tend towards "true" in face of floating point fluctuations. For example, I have another method, that given a line segment and a point, returns the closest location on the line segment to the given point. Currently, given any point outside the polygon and one of its edges, there are cases where the result is categorized as being inside by the method above, while other points are considered outside. I'd like to give it enough tolerance so that it always returns true in this situation. The way I've currently solved the problem is an hack, which consists of using an external library to inflate the polygon by a few pixels, and performing the tests on the inflated polygon, but I'd really like to replace this with a proper solution.

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• How to perform simple collision detection?

  - by Rob

  Imagine two squares sitting side by side, both level with the ground like so: A simple way to detect if one is hitting the other is to compare the location of each side. They are touching if all of the following are false: The right square's left side is to the right of the left square's right side. The right square's right side is to the left of the left square's left side. The right square's bottom side is above the left square's top side. The right square's top side is below the left square's bottom side. If any of those are true, the squares are not touching. But consider a case like this, where one square is at a 45 degree angle: Is there an equally simple way to determine if those squares are touching?

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• exact point oh a rotating sphere

  - by nkint

  I have a sphere that represents the heart textured with real pictures. It's rotating about the x axis, and when user click down it has to show me the exact place he clicked on. For example if he clicked on Singapore and the system should be able to: understand that user clicked on the sphere (OK, I'll do it with unProject) understand where user clicked on the sphere (ray-sphere collision?) and take into account the rotation transform sphere-coordinate to some coordinate system good for some web-api service ask to api (OK, this is the simpler thing for me ;-) some advice?

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• Repairing back-facing triangles without user input

  - by LTR

  My 3D application works with user-imported 3D models. Frequently, those models have a few vertices facing into the wrong direction. (For example, there is a 3D roof and a few triangles of that roof are facing inside the building). I want to repair those automatically. We can make several assumptions about these 3D models: they are completely closed without holes, and the camera is always on the outside. My idea: Shoot 500 rays from every triangle outwards into all directions. From the back side of the triangle, all rays will hit another part of the model. From the front side, at least one ray will hit nothing. Is there a better algorithm? Are there any papers about something like this?

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• exact point on a rotating sphere

  - by nkint

  I have a sphere that represents the Earth textured with real pictures. It's rotating around the x axis, and when user click down it has to show me the exact place he clicked on. For example if he clicked on Singapore the system should be able to: understand that user clicked on the sphere (OK, I'll do it with unProject) understand where user clicked on the sphere (ray-sphere collision?) and take into account the rotation transform sphere-coordinate to some coordinate system good for some web-api service ask to api (OK, this is the simpler thing for me ;-) some advice?

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• Approach for packing 2D shapes while minimizing total enclosing area

  - by Dennis

  Not sure on my tags for this question, but in short .... I need to solve a problem of packing industrial parts into crates while minimizing total containing area. These parts are motors, or pumps, or custom-made components, and they have quite unusual shapes. For some, it may be possible to assume that a part === rectangular cuboid, but some are not so simple, i.e. they assume a shape more of that of a hammer or letter T. With those, (assuming 2D shape), by alternating direction of top & bottom, one can pack more objects into the same space, than if all tops were in the same direction. Crude example below with letter "T"-shaped parts: ***** xxxxx ***** x ***** *** ooo * x vs * x vs * x vs * x o * x * xxxxx * x * x o xxxxx xxx Right now we are solving the problem by something like this: using CAD software, make actual models of how things fit in crate boxes make estimates of actual crate dimensions & write them into Excel file (1) is crazy amount of work and as the result we have just a limited amount of possible entries in (2), the Excel file. The good things is that programming this is relatively easy. Given a combination of products to go into crates, we do a lookup, and if entry exists in the Excel (or Database), we bring it out. If it doesn't, we say "sorry, no data!". I don't necessarily want to go full force on making up some crazy algorithm that given geometrical part description can align, rotate, and figure out best part packing into a crate, given its shape, but maybe I do.. Question Well, here is my question: assuming that I can represent my parts as 2D (to be determined how), and that some parts look like letter T, and some parts look like rectangles, which algorithm can I use to give me a good estimate on the dimensions of the encompassing area, while ensuring that the parts are packed in a minimal possible area, to minimize crating/shipping costs? Are there approximation algorithms? Seeing how this can get complex, is there an existing library I could use? My thought / Approach My naive approach would be to define a way to describe position of parts, and place the first part, compute total enclosing area & dimensions. Then place 2nd part in 0 degree orientation, repeat, place it at 180 degree orientation, repeat (for my case I don't think 90 degree rotations will be meaningful due to long lengths of parts). Proceed using brute force "tacking on" other parts to the enclosing area until all parts are processed. I may have to shift some parts a tad (see 3rd pictorial example above with letters T). This adds a layer of 2D complexity rather than 1D. I am not sure how to approach this. One idea I have is genetic algorithms, but I think those will take up too much processing power and time. I will need to look out for shape collisions, as well as adding extra padding space, since we are talking about real parts with irregularities rather than perfect imaginary blocks. I'm afraid this can get geometrically messy fairly fast, and I'd rather keep things simple, if I can. But what if the best (practical) solution is to pack things into different crate boxes rather than just one? This can get a bit more tricky. There is human element involved as well, i.e. like parts can go into same box and are thus a constraint to be considered. Some parts that are not the same are sometimes grouped together for shipping and can be considered as a common grouped item. Sometimes customers want things shipped their way, which adds human element to constraints. so there will have to be some customization.

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• Equation / formula to determine an objects position on an ellipitcal path

  - by David Murphy

  I'm making a space game, as such I need objects to follow an elliptical path (orbit). I've worked out how to calculate all the important aspects of my orbits, the only remaining thing is how to have an object follow it. My Orbit class contains the major, minor (and by extension semi-major,semi-minor) lengths. The focii radius, area and circumference even. What is the equation to determine an objects x/y position (only need 2D) on an ellipse with a certain speed after a period of time. Basically, every frame I want to update the position based on the amount of elapsed time. I would like to have the speed along the path speed up and slow down according to the distance from the object it's orbiting, but not sure how to factor this in to the above given that at any point in time the speed has changed from it's previous speed. EDIT I can't answer my own question. But I found the question and answer is already on stackexchange: Kepler orbit : get position on the orbit over time

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• point to rectangle distance

  - by john smith

  I have a 2D rectangle with x, y position and it's height and width and a randomly positioned point nearby it. Is there a way to check if this point might collide with the rectangle if closer than a certain distance? like imagine an invisible radius outside of that point colliding with said rectangle. I have problems with this simply because it is not a square, it would be so much easier this way! Any help? Thanks in advance.

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• "LNK2001: unresolved external symbol" when trying to build my program

  - by random

  I get the following error(s) on my program that captures the mouse and then draws a line. Errors: 1>------ Build started: Project: Capture_Mouse_Line, Configuration: Debug Win32 ------ 1> main.cpp 1>main.obj : error LNK2001: unresolved external symbol "public: static long * Line::yc2" (?yc2@Line@@2PAJA) 1>main.obj : error LNK2001: unresolved external symbol "public: static long * Line::xc2" (?xc2@Line@@2PAJA) 1>main.obj : error LNK2001: unresolved external symbol "public: static long * Line::yc1" (?yc1@Line@@2PAJA) 1>main.obj : error LNK2001: unresolved external symbol "public: static long * Line::xc1" (?xc1@Line@@2PAJA) 1>MSVCRTD.lib(crtexe.obj) : error LNK2019: unresolved external symbol _main referenced in function ___tmainCRTStartup 1>D:\Visual C++ Projects\Capture_Mouse_Line\Debug\Capture_Mouse_Line.exe : fatal error LNK1120: 5 unresolved externals ========== Build: 0 succeeded, 1 failed, 0 up-to-date, 0 skipped ========== Here is my code: #include<allegro5\allegro.h> #include<allegro5\allegro_native_dialog.h> #include<allegro5\allegro_primitives.h> #include<Windows.h> #include<allegro5\allegro_windows.h> #ifndef WIDTH #define WIDTH 1440 #endif #ifndef HEIGHT #define HEIGHT 900 #endif class Line { public: static void ErasePreviousLine(); static void DrawLine(long* x, long* y,long* x2,long* y2); static bool Erasable(); static long* xc1; static long* yc1; static long* xc2; static long* yc2; }; void Line::ErasePreviousLine() { delete xc1; xc1 = NULL; delete yc1; yc1 = NULL; delete xc2; xc2 = NULL; delete yc2; yc2 = NULL; } bool Line::Erasable() { if(xc1 && yc1 && xc2 && yc2 == NULL) { return false; } else { return true; } } void Line::DrawLine(long* x,long* y,long* x2,long* y2) { if(!al_init_primitives_addon()) { al_show_native_message_box(NULL,NULL,NULL,"failed to initialize allegro", NULL,NULL); } xc1 = x; yc1 = y; xc2 = x2; yc2 = y2; al_draw_line((float)*xc1, (float)*yc1, (float)*xc2, (float)*yc2,al_map_rgb(255,0,255), 1); delete x; delete y; delete x2; delete y2; } LRESULT CALLBACK WndProc(HWND hwnd, UINT msg, WPARAM wParam, LPARAM lParam); int WINAPI WinMain(HINSTANCE hInstance,HINSTANCE hPrevInstance, LPSTR lpCmdLine, int nCmdShow) { MSG msg; ALLEGRO_DISPLAY* display = NULL; if(!al_init()) { al_show_native_message_box(NULL,NULL,NULL,"failed to initialize allegro", NULL,NULL); return -1; } display = al_create_display(WIDTH,HEIGHT); if(!display) { al_show_native_message_box(NULL,NULL,NULL,"failed to initialize display", NULL,NULL); return -1; } HWND hwnd = al_get_win_window_handle(display); if(hwnd == NULL) { MessageBox(NULL, "Window Creation Failed!", "Error!", MB_ICONEXCLAMATION | MB_OK); return 0; } ShowWindow(hwnd, nCmdShow); UpdateWindow(hwnd); while(GetMessage(&msg, NULL, 0, 0) > 0) { TranslateMessage(&msg); DispatchMessage(&msg); } return msg.wParam; } LRESULT CALLBACK WndProc(HWND hwnd, UINT msg, WPARAM wParam, LPARAM lParam) { static bool bIsCaptured; static POINTS ptsBegin; static POINTS ptsEnd; switch(msg) { case WM_LBUTTONDOWN: SetCapture(hwnd); bIsCaptured = true; ptsBegin = MAKEPOINTS(lParam); return 0; case WM_MOUSEMOVE: if(wParam & MK_LBUTTON) { if(!Line::Erasable()) { return 0; } Line::ErasePreviousLine(); ptsEnd = MAKEPOINTS(lParam); Line::DrawLine(new long(ptsBegin.x),new long(ptsBegin.y),new long(ptsEnd.x),new long(ptsEnd.y)); } break; case WM_LBUTTONUP: bIsCaptured = false; ReleaseCapture(); break; case WM_ACTIVATEAPP: { if(wParam == TRUE) { if(bIsCaptured){ SetCapture(hwnd);} } } break; } return 0; }

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• How to get distance from point to line with distinction between side of line?

  - by tesselode

  I'm making a 2d racing game. I'm taking the nice standard approach of having a set of points defining the center of the track and detecting whether the car is off the track by detecting its distance from the nearest point. The nicest way I've found of doing this is using the formula: d = |Am + Bn + C| / sqrt(A^2 + B^2) Unfortunately, to have proper collision resolution, I need to know which side of the line the car is hitting, but I can't do that with this formula because it only returns positive numbers. So my question is: is there a formula that will give me positive or negative numbers based on which side of the line the point is on? Can I just get rid of the absolute value in the formula or do I need to do something else?

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• How do you make a bullet ricochet off a vertical wall?

  - by Bagofsheep

  First things first. I am using C# with XNA. My game is top-down and the player can shoot bullets. I've managed to get the bullets to ricochet correctly off horizontal walls. Yet, despite using similar methods (e.g. http://stackoverflow.com/questions/3203952/mirroring-an-angle) and reading other answered questions about this subject I have not been able to get the bullets to ricochet off a vertical wall correctly. Any method I've tried has failed and sometimes made ricocheting off a horizontal wall buggy. Here is the collision code that calls the ricochet method: //Loop through returned tile rectangles from quad tree to test for wall collision. If a collision occurs perform collision logic. for (int r = 0; r < returnObjects.Count; r++) if (Bullets[i].BoundingRectangle.Intersects(returnObjects[r])) Bullets[i].doCollision(returnObjects[r]); Now here is the code for the doCollision method. public void doCollision(Rectangle surface) { if (Ricochet) doRicochet(surface); else Trash = true; } Finally, here is the code for the doRicochet method. public void doRicochet(Rectangle surface) { if (Position.X > surface.Left && Position.X < surface.Right) { //Mirror the bullet's angle. Rotation = -1 * Rotation; //Moves the bullet in the direction of its rotation by given amount. moveFaceDirection(Sprite.Width * BulletScale.X); } else if (Position.Y > surface.Top && Position.Y < surface.Bottom) { } } Since I am only dealing with vertical and horizontal walls at the moment, the if statements simply determine if the object is colliding from the right or left, or from the top or bottom. If the object's X position is within the boundaries of the tile's X boundaries (left and right sides), it must be colliding from the top, and vice verse. As you can see, the else if statement is empty and is where the correct code needs to go.

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• Point in Polygon, Ray Method: ending infinite line

  - by user2878528

  Having a bit of trouble with point in polygon collision detection using the ray method i.e. http://en.wikipedia.org/wiki/Point_in_polygon My problem is I need to give an end to the infinite line created. As with this infinite line I always get an even number of intersections and hence an invalid result. i.e. ignore or intersection to the right of the point being checked what I have what I want My current code based of Mecki awesome response for (int side = 0; side < vertices.Length; side++) { // Test if current side intersects with ray. // create infinite line // See: http://en.wikipedia.org/wiki/Linear_equation a = end_point.Y - start_point.Y; b = start_point.X - end_point.X; c = end_point.X * start_point.Y - start_point.X * end_point.Y; //insert points of vector d2 = a * vertices[side].Position.X + b * vertices[side].Position.Y + c; if (side - 1 < 0) d1 = a * vertices[vertices.Length - 1].Position.X + b * vertices[vertices.Length - 1].Position.Y + c; else d1 = a * vertices[side-1].Position.X + b * vertices[side-1].Position.Y + c; // If points have opposite sides, intersections++; if (d1 > 0 && d2 < 0 ) intersections++; if (d1 < 0 && d2 > 0 ) intersections++; } //if intersections odd inside = true if ((intersections % 2) == 1) inside = true; else inside = false;

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• How can I determine the first visible tile in an isometric perspective?

  - by alekop

  I am trying to render the visible portion of a diamond-shaped isometric map. The "world" coordinate system is a 2D Cartesian system, with the coordinates increasing diagonally (in terms of the view coordinate system) along the axes. The "view" coordinates are simply mouse offsets relative to the upper left corner of the view. My rendering algorithm works by drawing diagonal spans, starting from the upper right corner of the view and moving diagonally to the right and down, advancing to the next row when it reaches the right view edge. When the rendering loop reaches the lower left corner, it stops. There are functions to convert a point from view coordinates to world coordinates and then to map coordinates. Everything works when rendering from tile 0,0, but as the view scrolls around the rendering needs to start from a different tile. I can't figure out how to determine which tile is closest to the upper right corner. At the moment I am simply converting the coordinates of the upper right corner to map coordinates. This works as long as the view origin (upper right corner) is inside the world, but when approaching the edges of the map the starting tile coordinate obviously become invalid. I guess this boils down to asking "how can I find the intersection between the world X axis and the view X axis?"

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• Reflection velocity

  - by MindSeeker

  I'm trying to get a moving circular object to bounce (elastically) off of an immovable circular object. Am I doing this right? (The results look right, but I hate to trust that alone, and I can't find a tutorial that tackles this problem and includes the nitty gritty math/code to verify what I'm doing). If it is right, is there a better/faster/more elegant way to do this? Note that the object (this) is the moving circle, and the EntPointer object is the immovable circle. //take vector separating the two centers <x, y>, and then get unit vector of the result: MathVector2d unitnormal = MathVector2d(this -> Retxpos() - EntPointer -> Retxpos(), this -> Retypos() - EntPointer -> Retypos()).UnitVector(); //take tangent <-y, x> of the unitnormal: MathVector2d unittangent = MathVector2d(-unitnormal.ycomp, unitnormal.xcomp); MathVector2d V1 = MathVector2d(this -> Retxvel(), this -> Retyvel()); //Calculate the normal and tangent vector lengths of the velocity: (the normal changes, the tangent stays the same) double LengthNormal = DotProduct(unitnormal, V1); double LengthTangent = DotProduct(unittangent, V1); MathVector2d VelVecNewNormal = unitnormal.ScalarMultiplication(-LengthNormal); //the negative of what it was before MathVector2d VelVecNewTangent = unittangent.ScalarMultiplication(LengthTangent); //this stays the same MathVector2d NewVel = VectorAddition(VelVecNewNormal, VelVecNewTangent); //combine them xvel = NewVel.xcomp; //and then apply them yvel = NewVel.ycomp; Note also that this question is just about velocity, the position code is handled elsewhere (in other words, assume that this code is implemented at the exact moment that the circles begin to overlap). Thanks in advance for your help and time!

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• Voronoi regions of a (convex) polygon.

  - by Xavura

  I'm looking to add circle-polygon collisions to my Separating Axis Theorem collision detection. The metanet software tutorial (http://www.metanetsoftware.com/technique/tutorialA.html#section3) on SAT, which I discovered in the answer to a question I found when searching, talks about voronoi regions. I'm having trouble finding material on how I would calculate these regions for an arbitrary convex polygon and aleo how I would determine if a point is in one + which. The tutorial does contain source code but it's a .fla and I don't have Flash unfortunately.

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• What do ptLineDist and relativeCCW do?

  - by Fasih Khatib

  I saw these methods in the Line2D Java Docs but did not understand what they do? Javadoc for ptLineDist says: Returns the distance from a point to this line. The distance measured is the distance between the specified point and the closest point on the infinitely-extended line defined by this Line2D. If the specified point intersects the line, this method returns 0.0 Doc for relativeCCW says: Returns an indicator of where the specified point (PX, PY) lies with respect to the line segment from (X1, Y1) to (X2, Y2). The return value can be either 1, -1, or 0 and indicates in which direction the specified line must pivot around its first endpoint, (X1, Y1), in order to point at the specified point (PX, PY). A return value of 1 indicates that the line segment must turn in the direction that takes the positive X axis towards the negative Y axis. In the default coordinate system used by Java 2D, this direction is counterclockwise. A return value of -1 indicates that the line segment must turn in the direction that takes the positive X axis towards the positive Y axis. In the default coordinate system, this direction is clockwise. A return value of 0 indicates that the point lies exactly on the line segment. Note that an indicator value of 0 is rare and not useful for determining colinearity because of floating point rounding issues. If the point is colinear with the line segment, but not between the endpoints, then the value will be -1 if the point lies "beyond (X1, Y1)" or 1 if the point lies "beyond (X2, Y2)".

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