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Search found 702 results on 29 pages for 'geometry'.

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• Drawing a rectangular prism using opengl

  - 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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• Manually writing a dx11 tessellation shader

  - by Tudor

  I am looking for resources on what are the steps of manually implementing tessellation (I'm using Unity cg). Today it seems that it is all the rage to hide most of the gpu code far away and use rather rigid simplifications such as unity's SURFace shaders. And it seems useless unless you're doing supeficial stuff. A little background: I have procedurally generated meshes (using marching cubes) which have quality normals but no UVs and no Tangents. I have successfully written a custom vertex and fragment shader to do triplanar texture and bumpmap projection as well as some custom stuff (custom lighting, procedurally warping the texture for variation etc). I am using the GPU Gems book as reference. Now I need to implement tessellation, but It seems I must calculate the tangents at runtime by swizzling normals (ctrl+f this in gems: <normal.z, normal.y, -normal.x>) before the tessellator gets them. And I also need to keep my custom vert+frag setup (with my custom parameters/textures being passed between them) - so apparently I cannot use surface shaders. Can anyone provide some guidence?

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• Morph a sphere to a cube and a cube to a sphere with GLSL

  - by nkint

  I'm getting started with GLSL with quartz composer. I have a patch with a particle system in which each particle is mapped into a sphere with a blend value. With blend=0 particles are in random positions, blend=1 particles are in the sphere. The code is here: vec3 sphere(vec2 domain) { vec3 range; range.x = radius * cos(domain.y) * sin(domain.x); range.y = radius * sin(domain.y) * sin(domain.x); range.z = radius * cos(domain.x); return range; } // in main: vec2 p0 = gl_Vertex.xy * twopi; vec3 normal = sphere(p0);; vec3 r0 = radius * normal; vec3 vertex = r0; normal = normal * blend + gl_Normal * (1.0 - blend); vertex = vertex * blend + gl_Vertex.xyz * (1.0 - blend); I'd like the particle to be on a cube if blend=0 I've tried to find but I can't figure out some parametric equation for the cube. Maybe it is not the right way?

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• How to detect two moving shapes overlapped?

  - by user1389813

  Given a list of circles with its coordinates (x and y) that are moving every second in different direction (South-East, South-West, North-East and North-West), and the circle will change direction if it hits the wall sort of like bouncing, so how do we detect if any of them collide or overlap with each other ? I am not sure if we can use some data structures like a Binary Search Tree because since all the coordinates vary every seconds, so the tree will have to re-build accordingly. Or can we use Vertical Sweep Line Algorithm each time ? Any ideas on how to do this in a efficient way ?

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• morph a sphere to a cube and a a cube to a sphere with GLSL

  - by nkint

  hi i'm getting started with glsl with quartz composer. i have a patch with a particle system in which each particle is mapped into a sphere with a blend value. with blend=0 particles are in random positions, blend=1 particles are in the sphere. the code is here: vec3 sphere(vec2 domain) { vec3 range; range.x = radius * cos(domain.y) * sin(domain.x); range.y = radius * sin(domain.y) * sin(domain.x); range.z = radius * cos(domain.x); return range; } // in main: normal = sphere(p0); * blend + gl_Normal * (1.0 - blend); i'd like the particle to be on a cube if blend=0 i've tried to find but i can't figure out some parametric equation for the cube. mayebe it is not the right way?

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• OpenGL - have object follow mouse

  - by kevin james

  I want to have an object follow around my mouse on the screen in OpenGL. (I am also using GLEW, GLFW, and GLM). The best idea I've come up with is: Get the coordinates within the window with glfwGetCursorPos. The window was created with window = glfwCreateWindow( 1024, 768, "Test", NULL, NULL); and the code to get coordinates is double xpos, ypos; glfwGetCursorPos(window, &xpos, &ypos); Next, I use GLM unproject, to get the coordinates in "object space" glm::vec4 viewport = glm::vec4(0.0f, 0.0f, 1024.0f, 768.0f); glm::vec3 pos = glm::vec3(xpos, ypos, 0.0f); glm::vec3 un = glm::unProject(pos, View*Model, Projection, viewport); There are two potential problems I can already see. The viewport is fine, as the initial x,y, coordinates of the lower left are indeed 0,0, and it's indeed a 1024*768 window. However, the position vector I create doesn't seem right. The Z coordinate should probably not be zero. However, glfwGetCursorPos returns 2D coordinates, and I don't know how to go from there to the 3D window coordinates, especially since I am not sure what the 3rd dimension of the window coordinates even means (since computer screens are 2D). Then, I am not sure if I am using unproject correctly. Assume the View, Model, Projection matrices are all OK. If I passed in the correct position vector in Window coordinates, does the unproject call give me the coordinates in Object coordinates? I think it does, but the documentation is not clear. Finally, to each vertex of the object I want to follow the mouse around, I just increment the x coordinate by un[0], the y coordinate by -un[1], and the z coordinate by un[2]. However, since my position vector that is being unprojected is likely wrong, this is not giving good results; the object does move as my mouse moves, but it is offset quite a bit (i.e. moving the mouse a lot doesn't move the object that much, and the z coordinate is very large). I actually found that the z coordinate un[2] is always the same value no matter where my mouse is, probably because the position vector I pass into unproject always has a value of 0.0 for z. Edit: The (incorrectly) unprojected x-values range from about -0.552 to 0.552, and the y-values from about -0.411 to 0.411.

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• Finding the normals of an oriented bounding box?

  - by Milo

  Here is my problem. I'm working on the physics for my 2D game. All objects are oriented bounding boxes (OBB) based on the separate axis theorem. In order to do collision resolution, I need to be able to get an object out out of the object it is penetrating. To do this I need to find the normal of the face(s) that the other OBB is touching. Example: The small red OBB is a car lets say, and the big OBB is a static building. I need to determine the unit vector that is the normal of the building edge(s) the car is penetrating to get the car out of there. Here are my questions: How do I determine which edges the car is penetrating. I know how to determine the normal of an edge, but how do I know if I need (-dy, dx) or (dy, -dx)? In the case I'm demonstrating the car is penetrating 2 edges, which edge(s) do I use to get it out? Answers or help with any or all of these is greatly appreciated. Thank you

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• Calculating angle a segment forms with a ray

  - by kr1zz

  I am given a point C and a ray r starting there. I know the coordinates (xc, yc) of the point C and the angle theta the ray r forms with the horizontal, theta in (-pi, pi]. I am also given another point P of which I know the coordinates (xp, yp): how do I calculate the angle alpha that the segment CP forms with the ray r, alpha in (-pi, pi]? Some examples follow: I can use the the atan2 function.

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• How do graphics programmers deal with rendering vertices that don't change the image?

  - by canisrufus

  So, the title is a little awkward. I'll give some background, and then ask my question. Background: I work as a web GIS application developer, but in my spare time I've been playing with map rendering and improving data interchange formats. I work only in 2D space. One interesting issue I've encountered is that when you're rendering a polygon at a small scale (zoomed way out), many of the vertices are redundant. An extreme case would be that you have a polygon with 500,000 vertices that only takes up a single pixel. If you're sending this data to the browser, it would make sense to omit ~499,999 of those vertices. One way we achieve that is by rendering an image on a server and and sending it as a PNG: voila, it's a point. Sometimes, though, we want data sent to the browser where it can be rendered with SVG (or canvas, or webgl) so that it can be interactive. The problem: It turns out that, using modern geographic data sets, it's very easy to overload SVG's rendering abilities. In an effort to cope with those limitations, I'm trying to figure out how to visually losslessly reduce a data set for a given scale and map extent (and, if necessary, for a known map pixel width and height). I got a great reduction in data size just using the Douglas-Peucker algorithm, and I believe I was able to get it to keep the polygons true to within one pixel. Unfortunately, Douglas-Peucker doesn't preserve topology, so it changed how borders between polygons got rendered. I couldn't readily find other algorithms to try out and adapt to the purpose, but I don't have much CS/algorithm background and might not recognize them if I saw them.

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• converting a mouse click to a ray

  - by Will

  I have a perspective projection. When the user clicks on the screen, I want to compute the ray between the near and far planes that projects from the mouse point, so I can do some ray intersection code with my world. I am using my own matrix and vector and ray classes and they all work as expected. However, when I try and convert the ray to world coordinates my far always ends up as 0,0,0 and so my ray goes from the mouse click to the centre of the object space, rather than through it. (The x and y coordinates of near and far are identical, they differ only in the z coordinates where they are negatives of each other) GLint vp[4]; glGetIntegerv(GL_VIEWPORT,vp); matrix_t mv, p; glGetFloatv(GL_MODELVIEW_MATRIX,mv.f); glGetFloatv(GL_PROJECTION_MATRIX,p.f); const matrix_t inv = (mv*p).inverse(); const float unit_x = (2.0f*((float)(x-vp[0])/(vp[2]-vp[0])))-1.0f, unit_y = 1.0f-(2.0f*((float)(y-vp[1])/(vp[3]-vp[1]))); const vec_t near(vec_t(unit_x,unit_y,-1)*inv); const vec_t far(vec_t(unit_x,unit_y,1)*inv); ray = ray_t(near,far-near); What have I got wrong? (How do you unproject the mouse-point?)

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• Bot strategy in an arena

  - by joulesm

  I am writing the player's behavior for an arena game, and I'm wondering if you could offer some strategies. I'm writing it in Python, but I'm just interested in the high level game play. Here are the game aspects: Arena is a circle of a given size. The arena's size shrinks every round to help break any ties. Players are much smaller circles, and can be on teams of 1 or 2 players. Players attack by colliding with other players, and based on the physics of the collision (speed of both players, angle), one could force another player out of the arena. Once a player is out of the arena, they are out of the game (for that round). The goal is to be on the only team with players left in the arena. All other players have been pushed (through collisions or mistakes) out of the arena. It is possible for there to be no winner if the last two players exit the arena at the same time. Once the player has been programmed, the game just runs. There is no human intervention in the game. I'm thinking it's easiest to implement a few simple programmatic rules for my player to follow. For example, stay close to center of the arena, attack opponents from the inner side of the arena, etc. Are there any good simple game strategies? Would adding a random aspect to the game help? For example, to avoid predictability by the other team or something. Thanks in advance.

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• How do you turn a cube into a sphere?

  - by Tom Dalling

  I'm trying to make a quad sphere based on an article, which shows results like this: I can generate a cube correctly: But when I convert all the points according to this formula (from the page linked above): x = x * sqrtf(1.0 - (y*y/2.0) - (z*z/2.0) + (y*y*z*z/3.0)); y = y * sqrtf(1.0 - (z*z/2.0) - (x*x/2.0) + (z*z*x*x/3.0)); z = z * sqrtf(1.0 - (x*x/2.0) - (y*y/2.0) + (x*x*y*y/3.0)); My sphere looks like this: As you can see, the edges of the cube still poke out too far. The cube ranges from -1 to +1 on all axes, like the article says. Any ideas what is wrong?

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• Implementing 2D CSG (for collision shapes)?

  - by bluescrn

  Are there any simple (or well documented) algorithms for basic CSG operations on 2D polygons? I'm looking for a way to 'add' a number of overlapping 2D collision shapes. These may be convex or concave, but will be closed shapes, defined as a set of line segments, with no self-intersections. The use of this would be to construct a clean set of collision edges, for use with a 2D physics engine, from a scene consisting of many arbitrarily placed (and frequently overlapping) objects, each with their own collision shape. To begin with, I only need to 'add' shapes, but the ability to 'subtract', to create holes, may also be useful.

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• Find vertices of a convex hull

  - by Jeff Bullard

  I am attempting to do this within CGAL. From a 3D point cloud, find the convex hull, then loop over the finite facets of the convex hull and print each facet's vertices. It seems like there should be a straightforward way to do this; I would have expected that 3D polyhedra would own a vector of facet objects, each of which in turn would own a vector of its edges, each of which in turn would own a vector of its vertices, and that their would be some access through this hierarchy using iterators. But so far I have been unable to find a simple way to navigate through this hierarchy (if it exists).

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• 2D isometric: screen to tile coordinates

  - by Dr_Asik

  I'm writing an isometric 2D game and I'm having difficulty figuring precisely on which tile the cursor is. Here's a drawing: where xs and ys are screen coordinates (pixels), xt and yt are tile coordinates, W and H are tile width and tile height in pixels, respectively. My notation for coordinates is (y, x) which may be confusing, sorry about that. The best I could figure out so far is this: int xtemp = xs / (W / 2); int ytemp = ys / (H / 2); int xt = (xs - ys) / 2; int yt = ytemp + xt; This seems almost correct but is giving me a very imprecise result, making it hard to select certain tiles, or sometimes it selects a tile next to the one I'm trying to click on. I don't understand why and I'd like if someone could help me understand the logic behind this. Thanks!

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• Partial recalculation of visibility on a 2D uniform grid

  - by Martin Källman

  Problem Imagine that we have a 2D uniform grid of dimensions N x N. For this grid we have also pre-computed a visibility look-up table, e.g. with DDA, which answers the boolean query is cell X visible from cell Y? The look-up table is a complete graph KN of the cells V in the grid, with each edge E being a binary value denoting the visibility between its vertices. Question If any given cell has its visibility modified, is it possible to extract the subset Edelta of edges which must have their visibility recomputed due to the change, so as to avoid a full-on recomputation for the entire grid? (Which is N(N-1) / 2 or N2 depending on the implementation) Update If is not possible to solve thi in closed form, then maintaining a separate mapping of each cell and every cell pair who's line intersects said cell might also be an option. This obviously consumes more memory, but the data is static. The increased memory requirement could be reduced by introducing a hierarchy, subdividing the grid into smaller parts, and by doing so the above mapping can be reused for each sub-grid. This would come at a cost in terms of increased computation relative to the number of subdivisions; also requiring a resumable ray-casting algorithm.

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• How to limit click'n'drag movement to an area?

  - by Vexille

  I apologize for the somewhat generic title. I'm really don't have much clue about how to accomplish what I'm trying to do, which is making it harder even to research a possible solution. I'm trying to implement a path marker of sorts (maybe there's a most suitable name for it, but this is the best I could come up with). In front of the player there will be a path marker, which will determine how the player will move once he finishes planning his turn. The player may click and drag the marker to the position they choose, but the marker can only be moved within a defined working area (the gray bit). So I'm now stuck with two problems: First of all, how exactly should I define that workable area? I can imagine maybe two vectors that have the player as a starting point to form the workable angle, and maybe those two arcs could come from circles that have their center where the player is, but I definetly don't know how to put this all together. And secondly, after I've defined the area where the marker can be placed, how can I enforce that the marker should only stay within that area? For example, if the player clicks and drags the marker around, it may move freely within the working area, but must not leave the boundaries of the area. So for example, if the player starts dragging the marker upwards, it will move upwards until it hits he end of the working area (first diagram below), but if after that the player starts dragging sideways, the marker must follow the drag while still within the area (second diagram below). I hope this wasn't all too confusing. Thanks, guys.

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• Splitting Graph into distinct polygons in O(E) complexity

  - by Arthur Wulf White

  If you have seen my last question: trapped inside a Graph : Find paths along edges that do not cross any edges How do you split an entire graph into distinct shapes 'trapped' inside the graph(like the ones described in my last question) with good complexity? What I am doing now is iterating over all edges and then starting to traverse while always taking the rightmost turn. This does split the graph into distinct shapes. Then I eliminate all the excess shapes (that are repeats of previous shapes) and return the result. The complexity of this algorithm is O(E^2). I am wondering if I could do it in O(E) by removing edges I already traversed previously. My current implementation of that returns unexpected results.

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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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• Scanline filling of polygons that share edges and vertices

  - by Belgin

  In this picture (a perspective projection of an icosahedron), the scanline (red) intersects that vertex at the top. In an icosahedron each edge belongs to two triangles. From edge a, only one triangle is visible, the other one is in the back. Same for edge d. Also, in order to determine what color the current pixel should be, each polygon has a flag which can either be 'in' or 'out', depending upon where on the scanline we currently are. Flags are flipped according to the intersection of the scanline with the edges. Now, as we go from a to d (because all edges are intersected with the scanline at that vertex), this happens: the triangle behind triangle 1 and triangle 1 itself are set 'in', then 2 is set in and 1 is 'out', then 3 is set 'in', 2 is 'out' and finally 3 is 'out' and the one behind it is set 'in', which is not the desired behavior because we only need the triangles which are facing us to be set 'in', the rest should be 'out'. How do process the edges in the Active Edge List (a list of edges that are currently intersected by the scanline) so the right polys are set 'in'? Also, I should mention that the edges are unique, which means there exists an array of edges in the data structure of the icosahedron which are pointed to by edge pointers in each of the triangles.

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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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• Annoying flickering of vertices and edges (possible z-fighting)

  - by Belgin

  I'm trying to make a software z-buffer implementation, however, after I generate the z-buffer and proceed with the vertex culling, I get pretty severe discrepancies between the vertex depth and the depth of the buffer at their projected coordinates on the screen (i.e. zbuffer[v.xp][v.yp] != v.z, where xp and yp are the projected x and y coordinates of the vertex v), sometimes by a small fraction of a unit and sometimes by 2 or 3 units. Here's what I think is happening: Each triangle's data structure holds the plane's (that is defined by the triangle) coefficients (a, b, c, d) computed from its three vertices from their normal: void computeNormal(Vertex *v1, Vertex *v2, Vertex *v3, double *a, double *b, double *c) { double a1 = v1 -> x - v2 -> x; double a2 = v1 -> y - v2 -> y; double a3 = v1 -> z - v2 -> z; double b1 = v3 -> x - v2 -> x; double b2 = v3 -> y - v2 -> y; double b3 = v3 -> z - v2 -> z; *a = a2*b3 - a3*b2; *b = -(a1*b3 - a3*b1); *c = a1*b2 - a2*b1; } void computePlane(Poly *p) { double x = p -> verts[0] -> x; double y = p -> verts[0] -> y; double z = p -> verts[0] -> z; computeNormal(p -> verts[0], p -> verts[1], p -> verts[2], &p -> a, &p -> b, &p -> c); p -> d = p -> a * x + p -> b * y + p -> c * z; } The z-buffer just holds the smallest depth at the respective xy coordinate by somewhat casting rays to the polygon (I haven't quite got interpolation right yet so I'm using this slower method until I do) and determining the z coordinate from the reversed perspective projection formulas (which I got from here: double z = -(b*Ez*y + a*Ez*x - d*Ez)/(b*y + a*x + c*Ez - b*Ey - a*Ex); Where x and y are the pixel's coordinates on the screen; a, b, c, and d are the planes coefficients; Ex, Ey, and Ez are the eye's (camera's) coordinates. This last formula does not accurately give the exact vertices' z coordinate at their projected x and y coordinates on the screen, probably because of some floating point inaccuracy (i.e. I've seen it return something like 3.001 when the vertex's z-coordinate was actually 2.998). Here is the portion of code that hides the vertices that shouldn't be visible: for(i = 0; i < shape.nverts; ++i) { double dist = shape.verts[i].z; if(z_buffer[shape.verts[i].yp][shape.verts[i].xp].z < dist) shape.verts[i].visible = 0; else shape.verts[i].visible = 1; } How do I solve this issue? EDIT I've implemented the near and far planes of the frustum, with 24 bit accuracy, and now I have some questions: Is this what I have to do this in order to resolve the flickering? When I compare the z value of the vertex with the z value in the buffer, do I have to convert the z value of the vertex to z' using the formula, or do I convert the value in the buffer back to the original z, and how do I do that? What are some decent values for near and far? Thanks in advance.

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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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