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  • Converting convex hull to binary mask

    - by Jonas
    I want to generate a binary mask that has ones for all pixels inside and zeros for all pixels outside a volume. The volume is defined by the convex hull around a set of 3D coordinates (<100; some of the coordinates are inside the volume). I can get the convex hull using CONVHULLN, but how do I convert that into a binary mask? In case there is no good way to go via the convex hull, do you have any other idea how I could create the binary mask?

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  • Sort latitude and longitude coordinates into clockwise quadrangle

    - by Dave Jarvis
    Problem Users can provide up to four latitude and longitude coordinates, in any order. They do so with Google Maps. Using Google's Polygon API (v3), the coordinates they select should highlight the selected area between the four coordinates. Solutions and Searches http://stackoverflow.com/questions/242404/sort-four-points-in-clockwise-order Graham's scan seems too complicated for four coordinates Sort the coordinates into two arrays (one by latitude, the other longitude) ... then? Question How do you sort the coordinates in (counter-)clockwise order, using JavaScript? Code Here is what I have so far: // Ensures the markers are sorted: NW, NE, SE, SW function sortMarkers() { var ns = markers.slice( 0 ); var ew = markers.slice( 0 ); ew.sort( function( a, b ) { if( a.lat() < b.lat() ) { return -1; } else if( a.lat() > b.lat() ) { return 1; } return 0; }); ns.sort( function( a, b ) { if( a.lng() < b.lng() ) { return -1; } else if( a.lng() > b.lng() ) { return 1; } return 0; }); } What is a better approach? Thank you.

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  • Distance from a point to a polygon

    - by clwen
    I am trying to determine the distance from a point to a polygon in 2D space. The point can be inside or outside the polygon; The polygon can be convex or concave. If the point is within the polygon or outside the polygon with a distance smaller than a user-defined constant d, the procedure should return True; False otherwise. I have found a similar question: Distance from a point to a polyhedron or to a polygon. However, the space is 2D in my case and the polygon can be concave, so it's somehow different from that one. I suppose there should be a method simpler than offsetting the polygon by d and determining it's inside or outside the polygon. Any algorithm, code, or hints for me to google around would be appreciated.

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  • Find point which sum of distances to set of other points is minimal

    - by Pawel Markowski
    I have one set (X) of points (not very big let's say 1-20 points) and the second (Y), much larger set of points. I need to choose some point from Y which sum of distances to all points from X is minimal. I came up with an idea that I would treat X as a vertices of a polygon and find centroid of this polygon, and then I will choose a point from Y nearest to the centroid. But I'm not sure whether centroid minimizes sum of its distances to the vertices of polygon, so I'm not sure whether this is a good way? Is there any algorithm for solving this problem? Points are defined by geographical coordinates.

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  • GIS: line_locate_point() in Python

    - by miracle2k
    I'm pretty much a beginner when it comes to GIS, but I think I understand the basics - it doesn't seem to hard. But: All these acronyms and different libraries, GEOS, GDAL, PROJ, PCL, Shaply, OpenGEO, OGR, OGC, OWS and what not, each seemingly depending on any number of others, is slightly overwhelming me. Here's what I would like to do: Given a number of points and a linestring, I want to determine the location on the line closest to a certain point. In other words, what PostGIS's line_locate_point() does: http://postgis.refractions.net/documentation/manual-1.3/ch06.html#line%5Flocate%5Fpoint Except I want do use plain Python. Which library or libraries should I have a look at generally for doing these kinds of spatial calculations in Python, and is there one that specifically supports a line_locate_point() equivalent?

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  • Generate 2D cross-section polygon from 3D mesh

    - by nornagon
    I'm writing a game which uses 3D models to draw a scene (top-down orthographic projection), but a 2D physics engine to calculate response to collisions, etc. I have a few 3D assets for which I'd like to be able to automatically generate a hitbox by 'slicing' the 3D mesh with the X-Y plane and creating a polygon from the resultant edges. Google is failing me on this one (and not much helpful material on SO either). Suggestions?

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  • How can I group an array of rectangles into "Islands" of connected regions?

    - by Eric
    The problem I have an array of java.awt.Rectangles. For those who are not familiar with this class, the important piece of information is that they provide an .intersects(Rectangle b) function. I would like to write a function that takes this array of Rectangles, and breaks it up into groups of connected rectangles. Lets say for example, that these are my rectangles (constructor takes the arguments x, y, width,height): Rectangle[] rects = new Rectangle[] { new Rectangle(0, 0, 4, 2), //A new Rectangle(1, 1, 2, 4), //B new Rectangle(0, 4, 8, 2), //C new Rectangle(6, 0, 2, 2) //D } A quick drawing shows that A intersects B and B intersects C. D intersects nothing. A tediously drawn piece of ascii art does the job too: +-------+ +---+ ¦A+---+ ¦ ¦ D ¦ +-+---+-+ +---+ ¦ B ¦ +-+---+---------+ ¦ +---+ C ¦ +---------------+ Therefore, the output of my function should be: new Rectangle[][]{ new Rectangle[] {A,B,C}, new Rectangle[] {D} } The failed code This was my attempt at solving the problem: public List<Rectangle> getIntersections(ArrayList<Rectangle> list, Rectangle r) { List<Rectangle> intersections = new ArrayList<Rectangle>(); for(Rectangle rect : list) { if(r.intersects(rect)) { list.remove(rect); intersections.add(rect); intersections.addAll(getIntersections(list, rect)); } } return intersections; } public List<List<Rectangle>> mergeIntersectingRects(Rectangle... rectArray) { List<Rectangle> allRects = new ArrayList<Rectangle>(rectArray); List<List<Rectangle>> groups = new ArrayList<ArrayList<Rectangle>>(); for(Rectangle rect : allRects) { allRects.remove(rect); ArrayList<Rectangle> group = getIntersections(allRects, rect); group.add(rect); groups.add(group); } return groups; } Unfortunately, there seems to be an infinite recursion loop going on here. My uneducated guess would be that java does not like me doing this: for(Rectangle rect : allRects) { allRects.remove(rect); //... } Can anyone shed some light on the issue?

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  • Categorize the approximate shape of an array of Points in 3D Space

    - by user1295133
    I have a set of points in 3d space and I want to be able to categorize the shape that best fits them - cube, sphere, cylinder, planar (flat) etc. I've looked at supervised/machine learning but since I need first generate a large training data set that's not really suitable. My dream solution would be a java library with a wonderful magical function something like : public enum ShapeType { CUBE, SPHERE, CYLINDER, PLANAR } public ShapeType CategorizeShapeFromPoints( 3DPoint[] points ) However, any and all help will be appreciated. Thanks

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  • A simple algorithm for polygon intersection

    - by Elazar Leibovich
    I'm looking for a very simple algorithm for computing the polygon intersection/clipping. That is, given polygons P, Q, I wish to find polygon T which is contained in P and in Q, and I wish T to be maximal among all possible polygons. I don't mind the run time (I have a few very small polygons), I can also afford getting an approximation of the polygons' intersection (that is, a polygon with less points, but which is still contained in the polygons' intersection). But it is really important for me that the algorithm will be simple (cheaper testing) and preferably short (less code). edit: please note, I wish to obtain a polygon which represent the intersection. I don't need only a boolean answer to the question of whether the two polygons intersect.

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  • Fastest way of converting a quad to a triangle strip?

    - by Tina Brooks
    What is the fastest way of converting a quadrilateral (made up of foyr x,y points) to a triangle strip? I'm well aware of the general triangulation algorithms that exist, but I need a short, well optimized algorithm that deals with quadrilaterals only. My current algorithm does this, which works for most quads but still gets the points mixed up for some: #define fp(f) bounds.p##f /* Sort four points in ascending order by their Y values */ point_sort4_y(&fp(1), &fp(2), &fp(3), &fp(4)); /* Bottom two */ if (fminf(-fp(1).x, -fp(2).x) == -fp(2).x) { out_quad.p1 = fp(2); out_quad.p2 = fp(1); } else { out_quad.p1 = fp(1); out_quad.p2 = fp(2); } /* Top two */ if (fminf(-fp(3).x, -fp(4).x) == -fp(3).x) { out_quad.p3 = fp(3); out_quad.p4 = fp(4); } else { out_quad.p3 = fp(4); out_quad.p4 = fp(3); }

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  • How can I test if a point lies within a 3d shape with its surface defined by a point cloud?

    - by Ben
    Hi I have a collection of points which describe the surface of a shape that should be roughly spherical, and I need a method with which to determine if any other given point lies within this shape. I've previously been approximating the shape as an exact sphere, but this has proven too inaccurate and I need a more accurate method. Simplicity and speed is favourable over complete accuracy, a good approximation will suffice. I've come across techniques for converting a point cloud to a 3d mesh, but most things I have found have been very complicated, and I am looking for something as simple as possible. Any ideas? Many thanks, Ben.

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  • How to calculate the normal of points on a 3D cubic Bézier curve given normals for its start and end points?

    - by Robert
    I'm trying to render a "3D ribbon" using a single 3D cubic Bézier curve to describe it (the width of the ribbon is some constant). The first and last control points have a normal vector associated with them (which are always perpendicular to the tangents at those points, and describe the surface normal of the ribbon at those points), and I'm trying to smoothly interpolate the normal vector over the course of the curve. For example, given a curve which forms the letter 'C', with the first and last control points both having surface normals pointing upwards, the ribbon should start flat, parallel to the ground, slowly turn, and then end flat again, facing the same way as the first control point. To do this "smoothly", it would have to face outwards half-way through the curve. At the moment (for this case), I've only been able to get all the surfaces facing upwards (and not outwards in the middle), which creates an ugly transition in the middle. It's quite hard to explain, I've attached some images below of this example with what it currently looks like (all surfaces facing upwards, sharp flip in the middle) and what it should look like (smooth transition, surfaces slowly rotate round). Silver faces represent the front, black faces the back. Incorrect, what it currently looks like: Correct, what it should look like: All I really need is to be able to calculate this "hybrid normal vector" for any point on the 3D cubic bézier curve, and I can generate the polygons no problem, but I can't work out how to get them to smoothly rotate round as depicted. Completely stuck as to how to proceed!

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  • finding a point on an ellipse circumference which is inside a rectangle having center point, height

    - by Shlomi Assaf
    Hi all. I have a rectangle in .NET in which I draw an ellipse. I know the width, height and center point of that rectangle. Ofcourse the cetner point of the rectangle is also the center point of the ellipse. I know how to calculate a point on a circle, however I have no clue about an ellipse. I have those parameters and an angle, i need the point on the ellipse, can someone post the formula? I saw somewhere you need to calculate 2 points in which 2 raduises will go, the sum of the radiuses will be fixed and they will change in size accordingly. I dont know how to do that, I only have the rectange height, width and center point and ofcourse the angle I wish to find the point at. thanks for any help Shlomi

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  • Most "thorough" distribution of points around a circle

    - by hippietrail
    This question is intended to both abstract and focus one approach to my problem expressed at "Find the most colourful image in a collection of images". Imagine we have a set of circles, each has a number of points around its circumference. We want to find a metric that gives a higher rating to a circle with points distributed evenly around the circle. Circles with some points scattered through the full 360° are better but circles with far greater numbers of points in one area compared to a smaller number in another area are less good. The number of points is not limited. Two or more points may coincide. Coincidental points are still relevant. A circle with one point at 0° and one point at 180° is better than a circle with 100 points at 0° and 1000 points at 180°. A circle with one point every degree around the circle is very good. A circle with a point every half degree around the circle is better. In my other (colour based question) it was suggested that standard deviation would be useful but with caveat. Is this a good suggestion and does it cope with the closeness of 359° to 1°?

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  • signed angle between two 3d vectors with same origin within the same plane? recipe?

    - by Advanced Customer
    Was looking through the web for an answer but it seems like there is no clear recipe for it. What I need is a signed angle of rotation between two vectors Va and Vb lying within the same 3D plane and having the same origin knowing that: the plane contatining both vectors is an arbitrary and is not parallel to XY or any other of cardinal planes Vn - is a plane normal both vectors along with the normal have the same origin O = { 0, 0, 0 } Va - is a reference for measuring the left handed rotation at Vn The angle should be measured in such a way so if the plane would be XY plane the Va would stand for X axis unit vector of it. I guess I should perform a kind of coordinate space transformation by using the Va as the X-axis and the cross product of Vb and Vn as the Y-axis and then just using some 2d method like with atan2() or something. Any ideas? Formulas?

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  • What algorithm can I use to determine points within a semi-circle?

    - by khayman218
    I have a list of two-dimensional points and I want to obtain which of them fall within a semi-circle. Originally, the target shape was a rectangle aligned with the x and y axis. So the current algorithm sorts the pairs by their X coord and binary searches to the first one that could fall within the rectangle. Then it iterates over each point sequentially. It stops when it hits one that is beyond both the X and Y upper-bound of the target rectangle. This does not work for a semi-circle as you cannot determine an effective upper/lower x and y bounds for it. The semi-circle can have any orientation. Worst case, I will find the least value of a dimension (say x) in the semi-circle, binary search to the first point which is beyond it and then sequentially test the points until I get beyond the upper bound of that dimension. Basically testing an entire band's worth of points on the grid. The problem being this will end up checking many points which are not within the bounds.

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  • drawing circle without floating point calculation

    - by zaharpopov
    This is common interview question (according to some interview sites) but I can find no normal answers in Internet - some are wrong and some point to complex theory I expect not looked for in interview (like Bressenham algorithm). The question is simple: The circle equation is: x^2 + y^2 = R^2. Given R, draw 0,0-centered circle as best as possible without using any floating point (no trigo, square roots, and so on, only integers)

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  • How to convert any text/font to its bezier path representation?

    - by yizzreel
    I have a bezier path library to draw complex bezier paths without problem. Now, I need to know how to read a text or font and extract its path information to draw it as a path instead of as text. I came across a C applicaiton, FontForge. It does exactly what I need, picks any font and extract its path information. But what I need to know is how it does it to add that feature to my drawing library.

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  • Prims vs Polys: what are the pros and cons of each?

    - by Richard Inglis
    I've noticed that most 3d gaming/rendering environments represent solids as a mesh of (usually triangular) 3d polygons. However some examples, such as Second Life, or PovRay use solids built from a set of 3d primitives (cube, sphere, cone, torus etc) on which various operations can be performed to create more complex shapes. So my question is: why choose one method over the other for representing 3d data? I can see there might be benefits for complex ray-tracing operations to be able to describe a surface as a single mathematical function (like PovRay does), but SL surely isn't attempting anything so ambitious with their rendering engine. Equally, I can imagine it might be more bandwidth-efficient to serve descriptions of generalised solids instead of arbitrary meshes, but is it really worth the downside that SL suffers from (ie modelling stuff is really hard, and usually the results are ugly) - was this just a bad decision made early in SL's development that they're now stuck with? Or is it an artefact of what's easiest to implement in OpenGL?

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