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  • Shortest distance between a point and a line segment

    - by Eli Courtwright
    I need a basic function to find the shortest distance between a point and a line segment. Feel free to write the solution in any language you want; I can translate it into what I'm using (Javascript). EDIT: My line segment is defined by two endpoints. So my line segment AB is defined by the two points A (x1,y1) and B (x2,y2). I'm trying to find the distance between this line segment and a point C (x3,y3). My geometry skills are rusty, so the examples I've seen are confusing, I'm sorry to admit.

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  • Shortest distance between a point and a line segment

    - by Eli Courtwright
    I need a basic function to find the shortest distance between a point and a line segment. Feel free to write the solution in any language you want; I can translate it into what I'm using (Javascript). EDIT: My line segment is defined by two endpoints. So my line segment AB is defined by the two points A (x1,y1) and B (x2,y2). I'm trying to find the distance between this line segment and a point C (x3,y3). My geometry skills are rusty, so the examples I've seen are confusing, I'm sorry to admit.

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  • Shortest distance between two line segments

    - by Frank
    I need a function to find the shortest distance between two line segments. A line segment is defined by two endpoints. So for example one of my line segments (AB) would be defined by the two points A (x1,y1) and B (x2,y2) and the other (CD) would be defined by the two points C (x1,y1) and D (x2,y2). Feel free to write the solution in any language you want and I can translate it into javascript. Please keep in mind my geometry skills are pretty rusty. I have already seen http://stochastix.wordpress.com/2008/12/28/distance-between-two-lines/ and I am not sure how to translate this into a function. Thank you so much for help.

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  • How does Silverlight Image Clipping work?

    - by TreeUK
    I've got a very large image which I'd like to use for sprite techniques (à la css image sprites). I've got the code below: <Image x:Name="testImage" Width="24" Height="12" Source="../Resources/Images/sprites.png"> <Image.Clip> <RectangleGeometry Rect="258,10632,24,12" /> </Image.Clip> </Image> This clips the source image to 24x12 at the relative position of 258, 10632 in the source image. The problem is that I want the cropped image to show at 0,0 in the testImage whereas it shows it at 258, 10632. It's using the geometry as a cutting guide but also as a layout guide. Anyone have any idea how this should be done? if at all. Conclusion: There seems to be no good way of doing this at present, Graeme's solution seems to be the closest to achieving this with Silverlight 2.0. That said, if anyone knows of a better way of doing this, please reply with an answer.

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  • Drawing an honeycomb with as3

    - by vitto
    Hi, I'm trying to create an honeycomb with as3 but I have some problem on cells positioning. I've already created the cells (not with code) and for cycled them to a funcion and send to it the parameters which what I thought was need (the honeycomb cell is allready on a sprite container in the center of the stage). to see the structure of the cycle and which parameters passes, please see the example below, the only thing i calculate in placeCell is the angle which I should obtain directly inside tha called function Note: the angle is reversed but it isn't important, and the color are useful in example only for visually divide cases. My for cycle calls placeCell and passes cell, current_case, counter (index) and the honeycomb cell_lv (cell level). I thought it was what i needed but I'm not skilled in geometry and trigonometry, so I don't know how to position cells correctly: function placeCell (cell:Sprite, current_case:int, counter:int, cell_lv:int):void { var margin:int = 2; var angle:Number = (360 / (cell_lv * 6)) * (current_case + counter); var radius:Number = (cell.width + margin) * cell_lv; cell.x = radius * Math.cos (angle); cell.y = radius * Math.sin (angle); trace ("LV " + cell_lv + " current_case " + current_case + " counter " + counter + " angle " + angle + " radius " + radius) } how can I do to solve it?

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  • Camera for 2.5D Game

    - by me--
    I'm hoping someone can explain this to me like I'm 5, because I've been struggling with this for hours and simply cannot understand what I'm doing wrong. I've written a Camera class for my 2.5D game. The intention is to support world and screen spaces like this: The camera is the black thing on the right. The +Z axis is upwards in that image, with -Z heading downwards. As you can see, both world space and screen space have (0, 0) at their top-left. I started writing some unit tests to prove that my camera was working as expected, and that's where things started getting...strange. My tests plot coordinates in world, view, and screen spaces. Eventually I will use image comparison to assert that they are correct, but for now my test just displays the result. The render logic uses Camera.ViewMatrix to transform world space to view space, and Camera.WorldPointToScreen to transform world space to screen space. Here is an example test: [Fact] public void foo() { var camera = new Camera(new Viewport(0, 0, 250, 100)); DrawingVisual worldRender; DrawingVisual viewRender; DrawingVisual screenRender; this.Render(camera, out worldRender, out viewRender, out screenRender, new Vector3(30, 0, 0), new Vector3(30, 40, 0)); this.ShowRenders(camera, worldRender, viewRender, screenRender); } And here's what pops up when I run this test: World space looks OK, although I suspect the z axis is going into the screen instead of towards the viewer. View space has me completely baffled. I was expecting the camera to be sitting above (0, 0) and looking towards the center of the scene. Instead, the z axis seems to be the wrong way around, and the camera is positioned in the opposite corner to what I expect! I suspect screen space will be another thing altogether, but can anyone explain what I'm doing wrong in my Camera class? UPDATE I made some progress in terms of getting things to look visually as I expect, but only through intuition: not an actual understanding of what I'm doing. Any enlightenment would be greatly appreciated. I realized that my view space was flipped both vertically and horizontally compared to what I expected, so I changed my view matrix to scale accordingly: this.viewMatrix = Matrix.CreateLookAt(this.location, this.target, this.up) * Matrix.CreateScale(this.zoom, this.zoom, 1) * Matrix.CreateScale(-1, -1, 1); I could combine the two CreateScale calls, but have left them separate for clarity. Again, I have no idea why this is necessary, but it fixed my view space: But now my screen space needs to be flipped vertically, so I modified my projection matrix accordingly: this.projectionMatrix = Matrix.CreatePerspectiveFieldOfView(0.7853982f, viewport.AspectRatio, 1, 2) * Matrix.CreateScale(1, -1, 1); And this results in what I was expecting from my first attempt: I have also just tried using Camera to render sprites via a SpriteBatch to make sure everything works there too, and it does. But the question remains: why do I need to do all this flipping of axes to get the space coordinates the way I expect? UPDATE 2 I've since improved my rendering logic in my test suite so that it supports geometries and so that lines get lighter the further away they are from the camera. I wanted to do this to avoid optical illusions and to further prove to myself that I'm looking at what I think I am. Here is an example: In this case, I have 3 geometries: a cube, a sphere, and a polyline on the top face of the cube. Notice how the darkening and lightening of the lines correctly identifies those portions of the geometries closer to the camera. If I remove the negative scaling I had to put in, I see: So you can see I'm still in the same boat - I still need those vertical and horizontal flips in my matrices to get things to appear correctly. In the interests of giving people a repro to play with, here is the complete code needed to generate the above. If you want to run via the test harness, just install the xunit package: Camera.cs: using Microsoft.Xna.Framework; using Microsoft.Xna.Framework.Graphics; using System.Diagnostics; public sealed class Camera { private readonly Viewport viewport; private readonly Matrix projectionMatrix; private Matrix? viewMatrix; private Vector3 location; private Vector3 target; private Vector3 up; private float zoom; public Camera(Viewport viewport) { this.viewport = viewport; // for an explanation of the negative scaling, see: http://gamedev.stackexchange.com/questions/63409/ this.projectionMatrix = Matrix.CreatePerspectiveFieldOfView(0.7853982f, viewport.AspectRatio, 1, 2) * Matrix.CreateScale(1, -1, 1); // defaults this.location = new Vector3(this.viewport.Width / 2, this.viewport.Height, 100); this.target = new Vector3(this.viewport.Width / 2, this.viewport.Height / 2, 0); this.up = new Vector3(0, 0, 1); this.zoom = 1; } public Viewport Viewport { get { return this.viewport; } } public Vector3 Location { get { return this.location; } set { this.location = value; this.viewMatrix = null; } } public Vector3 Target { get { return this.target; } set { this.target = value; this.viewMatrix = null; } } public Vector3 Up { get { return this.up; } set { this.up = value; this.viewMatrix = null; } } public float Zoom { get { return this.zoom; } set { this.zoom = value; this.viewMatrix = null; } } public Matrix ProjectionMatrix { get { return this.projectionMatrix; } } public Matrix ViewMatrix { get { if (this.viewMatrix == null) { // for an explanation of the negative scaling, see: http://gamedev.stackexchange.com/questions/63409/ this.viewMatrix = Matrix.CreateLookAt(this.location, this.target, this.up) * Matrix.CreateScale(this.zoom) * Matrix.CreateScale(-1, -1, 1); } return this.viewMatrix.Value; } } public Vector2 WorldPointToScreen(Vector3 point) { var result = viewport.Project(point, this.ProjectionMatrix, this.ViewMatrix, Matrix.Identity); return new Vector2(result.X, result.Y); } public void WorldPointsToScreen(Vector3[] points, Vector2[] destination) { Debug.Assert(points != null); Debug.Assert(destination != null); Debug.Assert(points.Length == destination.Length); for (var i = 0; i < points.Length; ++i) { destination[i] = this.WorldPointToScreen(points[i]); } } } CameraFixture.cs: using Microsoft.Xna.Framework.Graphics; using System; using System.Collections.Generic; using System.Linq; using System.Windows; using System.Windows.Controls; using System.Windows.Media; using Xunit; using XNA = Microsoft.Xna.Framework; public sealed class CameraFixture { [Fact] public void foo() { var camera = new Camera(new Viewport(0, 0, 250, 100)); DrawingVisual worldRender; DrawingVisual viewRender; DrawingVisual screenRender; this.Render( camera, out worldRender, out viewRender, out screenRender, new Sphere(30, 15) { WorldMatrix = XNA.Matrix.CreateTranslation(155, 50, 0) }, new Cube(30) { WorldMatrix = XNA.Matrix.CreateTranslation(75, 60, 15) }, new PolyLine(new XNA.Vector3(0, 0, 0), new XNA.Vector3(10, 10, 0), new XNA.Vector3(20, 0, 0), new XNA.Vector3(0, 0, 0)) { WorldMatrix = XNA.Matrix.CreateTranslation(65, 55, 30) }); this.ShowRenders(worldRender, viewRender, screenRender); } #region Supporting Fields private static readonly Pen xAxisPen = new Pen(Brushes.Red, 2); private static readonly Pen yAxisPen = new Pen(Brushes.Green, 2); private static readonly Pen zAxisPen = new Pen(Brushes.Blue, 2); private static readonly Pen viewportPen = new Pen(Brushes.Gray, 1); private static readonly Pen nonScreenSpacePen = new Pen(Brushes.Black, 0.5); private static readonly Color geometryBaseColor = Colors.Black; #endregion #region Supporting Methods private void Render(Camera camera, out DrawingVisual worldRender, out DrawingVisual viewRender, out DrawingVisual screenRender, params Geometry[] geometries) { var worldDrawingVisual = new DrawingVisual(); var viewDrawingVisual = new DrawingVisual(); var screenDrawingVisual = new DrawingVisual(); const int axisLength = 15; using (var worldDrawingContext = worldDrawingVisual.RenderOpen()) using (var viewDrawingContext = viewDrawingVisual.RenderOpen()) using (var screenDrawingContext = screenDrawingVisual.RenderOpen()) { // draw lines around the camera's viewport var viewportBounds = camera.Viewport.Bounds; var viewportLines = new Tuple<int, int, int, int>[] { Tuple.Create(viewportBounds.Left, viewportBounds.Bottom, viewportBounds.Left, viewportBounds.Top), Tuple.Create(viewportBounds.Left, viewportBounds.Top, viewportBounds.Right, viewportBounds.Top), Tuple.Create(viewportBounds.Right, viewportBounds.Top, viewportBounds.Right, viewportBounds.Bottom), Tuple.Create(viewportBounds.Right, viewportBounds.Bottom, viewportBounds.Left, viewportBounds.Bottom) }; foreach (var viewportLine in viewportLines) { var viewStart = XNA.Vector3.Transform(new XNA.Vector3(viewportLine.Item1, viewportLine.Item2, 0), camera.ViewMatrix); var viewEnd = XNA.Vector3.Transform(new XNA.Vector3(viewportLine.Item3, viewportLine.Item4, 0), camera.ViewMatrix); var screenStart = camera.WorldPointToScreen(new XNA.Vector3(viewportLine.Item1, viewportLine.Item2, 0)); var screenEnd = camera.WorldPointToScreen(new XNA.Vector3(viewportLine.Item3, viewportLine.Item4, 0)); worldDrawingContext.DrawLine(viewportPen, new Point(viewportLine.Item1, viewportLine.Item2), new Point(viewportLine.Item3, viewportLine.Item4)); viewDrawingContext.DrawLine(viewportPen, new Point(viewStart.X, viewStart.Y), new Point(viewEnd.X, viewEnd.Y)); screenDrawingContext.DrawLine(viewportPen, new Point(screenStart.X, screenStart.Y), new Point(screenEnd.X, screenEnd.Y)); } // draw axes var axisLines = new Tuple<int, int, int, int, int, int, Pen>[] { Tuple.Create(0, 0, 0, axisLength, 0, 0, xAxisPen), Tuple.Create(0, 0, 0, 0, axisLength, 0, yAxisPen), Tuple.Create(0, 0, 0, 0, 0, axisLength, zAxisPen) }; foreach (var axisLine in axisLines) { var viewStart = XNA.Vector3.Transform(new XNA.Vector3(axisLine.Item1, axisLine.Item2, axisLine.Item3), camera.ViewMatrix); var viewEnd = XNA.Vector3.Transform(new XNA.Vector3(axisLine.Item4, axisLine.Item5, axisLine.Item6), camera.ViewMatrix); var screenStart = camera.WorldPointToScreen(new XNA.Vector3(axisLine.Item1, axisLine.Item2, axisLine.Item3)); var screenEnd = camera.WorldPointToScreen(new XNA.Vector3(axisLine.Item4, axisLine.Item5, axisLine.Item6)); worldDrawingContext.DrawLine(axisLine.Item7, new Point(axisLine.Item1, axisLine.Item2), new Point(axisLine.Item4, axisLine.Item5)); viewDrawingContext.DrawLine(axisLine.Item7, new Point(viewStart.X, viewStart.Y), new Point(viewEnd.X, viewEnd.Y)); screenDrawingContext.DrawLine(axisLine.Item7, new Point(screenStart.X, screenStart.Y), new Point(screenEnd.X, screenEnd.Y)); } // for all points in all geometries to be rendered, find the closest and furthest away from the camera so we can lighten lines that are further away var distancesToAllGeometrySections = from geometry in geometries let geometryViewMatrix = geometry.WorldMatrix * camera.ViewMatrix from section in geometry.Sections from point in new XNA.Vector3[] { section.Item1, section.Item2 } let viewPoint = XNA.Vector3.Transform(point, geometryViewMatrix) select viewPoint.Length(); var furthestDistance = distancesToAllGeometrySections.Max(); var closestDistance = distancesToAllGeometrySections.Min(); var deltaDistance = Math.Max(0.000001f, furthestDistance - closestDistance); // draw each geometry for (var i = 0; i < geometries.Length; ++i) { var geometry = geometries[i]; // there's probably a more correct name for this, but basically this gets the geometry relative to the camera so we can check how far away each point is from the camera var geometryViewMatrix = geometry.WorldMatrix * camera.ViewMatrix; // we order roughly by those sections furthest from the camera to those closest, so that the closer ones "overwrite" the ones further away var orderedSections = from section in geometry.Sections let startPointRelativeToCamera = XNA.Vector3.Transform(section.Item1, geometryViewMatrix) let endPointRelativeToCamera = XNA.Vector3.Transform(section.Item2, geometryViewMatrix) let startPointDistance = startPointRelativeToCamera.Length() let endPointDistance = endPointRelativeToCamera.Length() orderby (startPointDistance + endPointDistance) descending select new { Section = section, DistanceToStart = startPointDistance, DistanceToEnd = endPointDistance }; foreach (var orderedSection in orderedSections) { var start = XNA.Vector3.Transform(orderedSection.Section.Item1, geometry.WorldMatrix); var end = XNA.Vector3.Transform(orderedSection.Section.Item2, geometry.WorldMatrix); var viewStart = XNA.Vector3.Transform(start, camera.ViewMatrix); var viewEnd = XNA.Vector3.Transform(end, camera.ViewMatrix); worldDrawingContext.DrawLine(nonScreenSpacePen, new Point(start.X, start.Y), new Point(end.X, end.Y)); viewDrawingContext.DrawLine(nonScreenSpacePen, new Point(viewStart.X, viewStart.Y), new Point(viewEnd.X, viewEnd.Y)); // screen rendering is more complicated purely because I wanted geometry to fade the further away it is from the camera // otherwise, it's very hard to tell whether the rendering is actually correct or not var startDistanceRatio = (orderedSection.DistanceToStart - closestDistance) / deltaDistance; var endDistanceRatio = (orderedSection.DistanceToEnd - closestDistance) / deltaDistance; // lerp towards white based on distance from camera, but only to a maximum of 90% var startColor = Lerp(geometryBaseColor, Colors.White, startDistanceRatio * 0.9f); var endColor = Lerp(geometryBaseColor, Colors.White, endDistanceRatio * 0.9f); var screenStart = camera.WorldPointToScreen(start); var screenEnd = camera.WorldPointToScreen(end); var brush = new LinearGradientBrush { StartPoint = new Point(screenStart.X, screenStart.Y), EndPoint = new Point(screenEnd.X, screenEnd.Y), MappingMode = BrushMappingMode.Absolute }; brush.GradientStops.Add(new GradientStop(startColor, 0)); brush.GradientStops.Add(new GradientStop(endColor, 1)); var pen = new Pen(brush, 1); brush.Freeze(); pen.Freeze(); screenDrawingContext.DrawLine(pen, new Point(screenStart.X, screenStart.Y), new Point(screenEnd.X, screenEnd.Y)); } } } worldRender = worldDrawingVisual; viewRender = viewDrawingVisual; screenRender = screenDrawingVisual; } private static float Lerp(float start, float end, float amount) { var difference = end - start; var adjusted = difference * amount; return start + adjusted; } private static Color Lerp(Color color, Color to, float amount) { var sr = color.R; var sg = color.G; var sb = color.B; var er = to.R; var eg = to.G; var eb = to.B; var r = (byte)Lerp(sr, er, amount); var g = (byte)Lerp(sg, eg, amount); var b = (byte)Lerp(sb, eb, amount); return Color.FromArgb(255, r, g, b); } private void ShowRenders(DrawingVisual worldRender, DrawingVisual viewRender, DrawingVisual screenRender) { var itemsControl = new ItemsControl(); itemsControl.Items.Add(new HeaderedContentControl { Header = "World", Content = new DrawingVisualHost(worldRender)}); itemsControl.Items.Add(new HeaderedContentControl { Header = "View", Content = new DrawingVisualHost(viewRender) }); itemsControl.Items.Add(new HeaderedContentControl { Header = "Screen", Content = new DrawingVisualHost(screenRender) }); var window = new Window { Title = "Renders", Content = itemsControl, ShowInTaskbar = true, SizeToContent = SizeToContent.WidthAndHeight }; window.ShowDialog(); } #endregion #region Supporting Types // stupidly simple 3D geometry class, consisting of a series of sections that will be connected by lines private abstract class Geometry { public abstract IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get; } public XNA.Matrix WorldMatrix { get; set; } } private sealed class Line : Geometry { private readonly XNA.Vector3 magnitude; public Line(XNA.Vector3 magnitude) { this.magnitude = magnitude; } public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get { yield return Tuple.Create(XNA.Vector3.Zero, this.magnitude); } } } private sealed class PolyLine : Geometry { private readonly XNA.Vector3[] points; public PolyLine(params XNA.Vector3[] points) { this.points = points; } public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get { if (this.points.Length < 2) { yield break; } var end = this.points[0]; for (var i = 1; i < this.points.Length; ++i) { var start = end; end = this.points[i]; yield return Tuple.Create(start, end); } } } } private sealed class Cube : Geometry { private readonly float size; public Cube(float size) { this.size = size; } public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get { var halfSize = this.size / 2; var frontBottomLeft = new XNA.Vector3(-halfSize, halfSize, -halfSize); var frontBottomRight = new XNA.Vector3(halfSize, halfSize, -halfSize); var frontTopLeft = new XNA.Vector3(-halfSize, halfSize, halfSize); var frontTopRight = new XNA.Vector3(halfSize, halfSize, halfSize); var backBottomLeft = new XNA.Vector3(-halfSize, -halfSize, -halfSize); var backBottomRight = new XNA.Vector3(halfSize, -halfSize, -halfSize); var backTopLeft = new XNA.Vector3(-halfSize, -halfSize, halfSize); var backTopRight = new XNA.Vector3(halfSize, -halfSize, halfSize); // front face yield return Tuple.Create(frontBottomLeft, frontBottomRight); yield return Tuple.Create(frontBottomLeft, frontTopLeft); yield return Tuple.Create(frontTopLeft, frontTopRight); yield return Tuple.Create(frontTopRight, frontBottomRight); // left face yield return Tuple.Create(frontTopLeft, backTopLeft); yield return Tuple.Create(backTopLeft, backBottomLeft); yield return Tuple.Create(backBottomLeft, frontBottomLeft); // right face yield return Tuple.Create(frontTopRight, backTopRight); yield return Tuple.Create(backTopRight, backBottomRight); yield return Tuple.Create(backBottomRight, frontBottomRight); // back face yield return Tuple.Create(backBottomLeft, backBottomRight); yield return Tuple.Create(backTopLeft, backTopRight); } } } private sealed class Sphere : Geometry { private readonly float radius; private readonly int subsections; public Sphere(float radius, int subsections) { this.radius = radius; this.subsections = subsections; } public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get { var latitudeLines = this.subsections; var longitudeLines = this.subsections; // see http://stackoverflow.com/a/4082020/5380 var results = from latitudeLine in Enumerable.Range(0, latitudeLines) from longitudeLine in Enumerable.Range(0, longitudeLines) let latitudeRatio = latitudeLine / (float)latitudeLines let longitudeRatio = longitudeLine / (float)longitudeLines let nextLatitudeRatio = (latitudeLine + 1) / (float)latitudeLines let nextLongitudeRatio = (longitudeLine + 1) / (float)longitudeLines let z1 = Math.Cos(Math.PI * latitudeRatio) let z2 = Math.Cos(Math.PI * nextLatitudeRatio) let x1 = Math.Sin(Math.PI * latitudeRatio) * Math.Cos(Math.PI * 2 * longitudeRatio) let y1 = Math.Sin(Math.PI * latitudeRatio) * Math.Sin(Math.PI * 2 * longitudeRatio) let x2 = Math.Sin(Math.PI * nextLatitudeRatio) * Math.Cos(Math.PI * 2 * longitudeRatio) let y2 = Math.Sin(Math.PI * nextLatitudeRatio) * Math.Sin(Math.PI * 2 * longitudeRatio) let x3 = Math.Sin(Math.PI * latitudeRatio) * Math.Cos(Math.PI * 2 * nextLongitudeRatio) let y3 = Math.Sin(Math.PI * latitudeRatio) * Math.Sin(Math.PI * 2 * nextLongitudeRatio) let start = new XNA.Vector3((float)x1 * radius, (float)y1 * radius, (float)z1 * radius) let firstEnd = new XNA.Vector3((float)x2 * radius, (float)y2 * radius, (float)z2 * radius) let secondEnd = new XNA.Vector3((float)x3 * radius, (float)y3 * radius, (float)z1 * radius) select new { First = Tuple.Create(start, firstEnd), Second = Tuple.Create(start, secondEnd) }; foreach (var result in results) { yield return result.First; yield return result.Second; } } } } #endregion }

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  • Extracting ""((Adj|Noun)+|((Adj|Noun)(Noun-Prep)?)(Adj|Noun))Noun"" from Text (Justeson & Katz, 1995)

    - by ssuhan
    I would like to query if it is possible to extract ((Adj|Noun)+|((Adj|Noun)(Noun-Prep)?)(Adj|Noun))Noun proposed by Justeson and Katz (1995) in R package openNLP? That is, I would like to use this linguistic filtering to extract candidate noun phrases. I cannot well understand its meaning. Could you do me a favor to explain it or transform such representation into R language. Many thanks. Maybe we can start the sample code from: library("openNLP") acq <- "This paper describes a novel optical thread plug gauge (OTPG) for internal thread inspection using machine vision. The OTPG is composed of a rigid industrial endoscope, a charge-coupled device camera, and a two degree-of-freedom motion control unit. A sequence of partial wall images of an internal thread are retrieved and reconstructed into a 2D unwrapped image. Then, a digital image processing and classification procedure is used to normalize, segment, and determine the quality of the internal thread." acqTag <- tagPOS(acq) acqTagSplit = strsplit(acqTag," ")

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  • Polygon packing 2D

    - by Ilnur
    Hi! I have problem of packing 2 arbitrary polygons. I.e. we have 2 arbitrary polygons. We are to find such placement of this polygons (we could make rotations and movements), when rectangle, which circumscribes this polygons has minimal area. I know, that this is a NP-complete problem. I want to choose an efficient algorithm for solving this problem. I' looking for No-Fit-Polygon approach. But I could't find anywhere the simple and clear algorithm for finding the NFP of two arbitrary polygons.

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  • understanding semcor corpus structure h

    - by Sharmila
    I'm learning NLP. I currently playing with Word Sense Disambiguation. I'm planning to use the semcor corpus as training data but I have trouble understanding the xml structure. I tried googling but did not get any resource describing the content structure of semcor. <s snum="1"> <wf cmd="ignore" pos="DT">The</wf> <wf cmd="done" lemma="group" lexsn="1:03:00::" pn="group" pos="NNP" rdf="group" wnsn="1">Fulton_County_Grand_Jury</wf> <wf cmd="done" lemma="say" lexsn="2:32:00::" pos="VB" wnsn="1">said</wf> <wf cmd="done" lemma="friday" lexsn="1:28:00::" pos="NN" wnsn="1">Friday</wf> <wf cmd="ignore" pos="DT">an</wf> <wf cmd="done" lemma="investigation" lexsn="1:09:00::" pos="NN" wnsn="1">investigation</wf> <wf cmd="ignore" pos="IN">of</wf> <wf cmd="done" lemma="atlanta" lexsn="1:15:00::" pos="NN" wnsn="1">Atlanta</wf> <wf cmd="ignore" pos="POS">'s</wf> <wf cmd="done" lemma="recent" lexsn="5:00:00:past:00" pos="JJ" wnsn="2">recent</wf> <wf cmd="done" lemma="primary_election" lexsn="1:04:00::" pos="NN" wnsn="1">primary_election</wf> <wf cmd="done" lemma="produce" lexsn="2:39:01::" pos="VB" wnsn="4">produced</wf> <punc>``</punc> <wf cmd="ignore" pos="DT">no</wf> <wf cmd="done" lemma="evidence" lexsn="1:09:00::" pos="NN" wnsn="1">evidence</wf> <punc>''</punc> <wf cmd="ignore" pos="IN">that</wf> <wf cmd="ignore" pos="DT">any</wf> <wf cmd="done" lemma="irregularity" lexsn="1:04:00::" pos="NN" wnsn="1">irregularities</wf> <wf cmd="done" lemma="take_place" lexsn="2:30:00::" pos="VB" wnsn="1">took_place</wf> <punc>.</punc> </s> I'm assuming wnsn is 'word sense'. Is it correct? What does the attribute lexsn mean? How does it map to wordnet? What does the attribute pn refer to? (third line) How is the rdf attribute assigned? (again third line) In general, what are the possible attributes?

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  • Java: remove-common-words-method in the API?

    - by HH
    Related: Forum post Before reinventing the wheel, I need to know whether such method exists. Stripping words according to a list such as list does not sound challenging but there are linguistic aspects, such as which words to stress the most in stripping, how about context?

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  • Compose synthetic English phrase that would contain 160 bits of recoverable information

    - by Alexander Gladysh
    I have 160 bits of random data. Just for fun, I want to generate pseudo-English phrase to "store" this information in. I want to be able to recover this information from the phrase. Note: This is not a security question, I don't care if someone else will be able to recover the information or even detect that it is there or not. Criteria for better phrases, from most important to the least: Short Unique Natural-looking The current approach, suggested here: Take three lists of 1024 nouns, verbs and adjectives each (picking most popular ones). Generate a phrase by the following pattern, reading 20 bits for each word: Noun verb adjective verb, Noun verb adjective verb, Noun verb adjective verb, Noun verb adjective verb. Now, this seems to be a good approach, but the phrase is a bit too long and a bit too dull. I have found a corpus of words here (Part of Speech Database). After some ad-hoc filtering, I calculated that this corpus contains, approximately 50690 usable adjectives 123585 nouns 15301 verbs This allows me to use up to 16 bits per adjective (actually 16.9, but I can't figure how to use fractional bits) 15 bits per noun 13 bits per verb For noun-verb-adjective-verb pattern this gives 57 bits per "sentence" in phrase. This means that, if I'll use all words I can get from this corpus, I can generate three sentences instead of four (160 / 57 ˜ 2.8). Noun verb adjective verb, Noun verb adjective verb, Noun verb adjective verb. Still a bit too long and dull. Any hints how can I improve it? What I see that I can try: Try to compress my data somehow before encoding. But since the data is completely random, only some phrases would be shorter (and, I guess, not by much). Improve phrase pattern, so it would look better. Use several patterns, using the first word in phrase to somehow indicate for future decoding which pattern was used. (For example, use the last letter or even the length of the word.) Pick pattern according to the first bytes of the data. ...I'm not that good with English to come up with better phrase patterns. Any suggestions? Use more linguistics in the pattern. Different tenses etc. ...I guess, I would need much better word corpus than I have now for that. Any hints where can I get a suitable one?

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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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  • Largest triangle from a set of points

    - by Faken
    I have a set of random points from which i want to find the largest triangle by area who's verticies are each on one of those points. So far I have figured out that the largest triangle's verticies will only lie on the outside points of the cloud of points (or the convex hull) so i have programmed a function to do just that (using Graham scan in nlogn time). However that's where I'm stuck. The only way I can figure out how to find the largest triangle from these points is to use brute force at n^3 time which is still acceptable in an average case as the convex hull algorithm usually kicks out the vast majority of points. However in a worst case scenario where points are on a circle, this method would fail miserably. Dose anyone know an algorithm to do this more efficiently? Note: I know that CGAL has this algorithm there but they do not go into any details on how its done. I don't want to use libraries, i want to learn this and program it myself (and also allow me to tweak it to exactly the way i want it to operate, just like the graham scan in which other implementations pick up collinear points that i don't want).

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  • Ray-triangle intersetion

    - by gamemaker
    Hello! How can I test intersesion ray and triangle, and if it exist how to get distance from ray origin to intersection point?? What optimization I can use, if in my program I've got to check 1 ray to ~10000 triangles ??

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  • Cuboid inside generic polyhedron

    - by DOFHandler
    I am searching for an efficient algorithm to find if a cuboid is completely inside or completely outside or (not-inside and not-outside) a generic (concave or convex) polyhedron. The polyhedron is defined by a list of 3D points and a list of facets. Each facet is defined by the subset of the contour points ordinated such as the right-hand normal points outward the solid. Any suggestion? Thank you

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  • Android: Find coordinates of a certain point X meters from my location moving towards the point I am

    - by Aidan
    Hi Guys, I'm constructing a geolocation based application and I'm trying to figure out a way to make my application realise when a user is facing the direction of the given location (a particular long / lat co-ord). I've done some Googling and checked the SDK but can't really find anything for such a thing. Does anyone know of a way? Example. Point A = Phones current location. Point B = A's orientation in relation to true north + 45 + max distance towards the direction your facing, Point C = A's orientation in relation to true north - 45 + max distance towards the direction your facing. So now you have a triangle constructed. pretty schweet huh? yeah.. I think so.. So now that I have my fancy Triangle I use something called Barycentric Coordinates ( http://en.wikipedia.org/wiki/Barycentric_coordinates_(mathematics) ). This will allow me to test another point and see if it is in the triangle. If it is, it means we're facing it AND it's within the right distance. So it should be displayed on screen. If I'm facing 90 degrees from true north. The distance it travels should be that direction. 90 degrees from true north. It should not be 100 degrees or something from true north! But the problem is I haven't yet figured out how I make the device realise it must go "out" the direction it is facing.

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  • How do I determine when two moving points become visible to each other?

    - by Devin Jeanpierre
    Suppose I have two points, Point1 and Point2. At any given time, these points may be at different positions-- they are not necessarily static. Point1 is located at some position at time t, and its position is defined by the continuous functions x1(t) and y1(t) giving the x and y coordinates at time t. These functions are not differentiable, they are constructed piecewise from line segments. Point2 is the same, with x2(t) and y2(t), each function having the same properties. The obstacles that might prevent visibility are simple (and immobile) polygons. How can I find the boundary points for visibility? i.e. there are two kinds of boundaries: where the points become visible, and become invisible. For a become-visible boundary i, there exists some ?0, such that for any real number a, a ? (i-?, i) , Point1 and Point2 are not visible (i.e. the line segment that connects (x1(a), y1(a)) to (x2(a), y2(x)) crosses some obstacles). For b ? (i, i+?) they are visible. And it is the other way around for becomes-invisible. But can I find such a precise boundary, and if so, how?

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  • Merging and splitting overlapping rectangles to produce non-overlapping ones

    - by uj
    I am looking for an algorithm as follows: Given a set of possibly overlapping rectangles (All of which are "not rotated", can be uniformly represented as (left,top,right,bottom) tuplets, etc...), it returns a minimal set of (non-rotated) non-overlapping rectangles, that occupy the same area. It seems simple enough at first glance, but prooves to be tricky (at least to be done efficiently). Are there some known methods for this/ideas/pointers? Methods for not necessarily minimal, but heuristicly small, sets, are interesting as well, so are methods that produce any valid output set at all.

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  • determine if line segment is inside polygon

    - by dato
    suppose we have simple polygon(without holes) with vertices (v0,v1,....vn) my aim is to determine if for given point p(x,y) any line segment connecting this point and any vertices of polygon is inside polygon or even for given two point p(x0,y0) `p(x1,y1)` line segment connecting these two point is inside polygon? i have searched many sites about this ,but i am still confused,generally i think we have to compare coordinates of vertices and by determing coordinates of which point is less or greater to another point's coordinates,we could determine location of any line segment,but i am not sure how correct is this,please help me

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  • What's a good library to do computational geometry (like CGAL) in a garbage-collected language?

    - by Squash Monster
    I need a library to handle computational geometry in a project, especially boolean operations, but just about every feature is useful. The best library I can find for this is CGAL, but this is the sort of project I would hesitate to make without garbage collection. What language/library pairs can you recommend? So far my best bet is importing CGAL into D. There is also a project for making Python bindings for CGAL, but it's very incomplete.

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  • Sort latitude and longitude coordinates into clockwise ordered quadrilateral

    - 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://www.geocodezip.com/map-markers_ConvexHull_Polygon.asp http://softsurfer.com/Archive/algorithm_0103/algorithm_0103.htm http://stackoverflow.com/questions/2374708/how-to-sort-points-in-a-google-maps-polygon-so-that-lines-do-not-cross http://stackoverflow.com/questions/242404/sort-four-points-in-clockwise-order http://en.literateprograms.org/Quickhull_%28Javascript%29 Graham's scan seems too complicated for four coordinates Sort the coordinates into two arrays (one by latitude, the other longitude) ... then? Jarvis March algorithm? 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.position.lat() < b.position.lat() ) { return -1; } else if( a.position.lat() > b.position.lat() ) { return 1; } return 0; }); ns.sort( function( a, b ) { if( a.position.lng() < b.position.lng() ) { return -1; } else if( a.position.lng() > b.position.lng() ) { return 1; } return 0; }); var nw; var ne; var se; var sw; if( ew.indexOf( ns[0] ) > 1 ) { nw = ns[0]; } else { ne = ns[0]; } if( ew.indexOf( ns[1] ) > 1 ) { nw = ns[1]; } else { ne = ns[1]; } if( ew.indexOf( ns[2] ) > 1 ) { sw = ns[2]; } else { se = ns[2]; } if( ew.indexOf( ns[3] ) > 1 ) { sw = ns[3]; } else { se = ns[3]; } markers[0] = nw; markers[1] = ne; markers[2] = se; markers[3] = sw; } What is a better approach? The recursive Convex Hull algorithm is overkill for four points in the data set. Thank you.

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  • Point in polygon OR point on polygon using LINQ

    - by wageoghe
    As noted in an earlier question, How to Zip enumerable with itself, I am working on some math algorithms based on lists of points. I am currently working on point in polygon. I have the code for how to do that and have found several good references here on SO, such as this link Hit test. So, I can figure out whether or not a point is in a polygon. As part of determining that, I want to determine if the point is actually on the polygon. This I can also do. If I can do all of that, what is my question you might ask? Can I do it efficiently using LINQ? I can already do something like the following (assuming a Pairwise extension method as described in my earlier question as well as in links to which my question/answers links, and assuming a Position type that has X and Y members). I have not tested much, so the lambda might not be 100% correct. Also, it does not take very small differences into account. public static PointInPolygonLocation PointInPolygon(IEnumerable<Position> pts, Position pt) { int numIntersections = pts.Pairwise( (p1, p2) => { if (p1.Y != p2.Y) { if ((p1.Y >= pt.Y && p2.Y < pt.Y) || (p1.Y < pt.Y && p2.Y >= pt.Y)) { if (p1.X < p1.X && p2.X < pt.X) { return 1; } if (p1.X < pt.X || p2.X < pt.X) { if (((pt.Y - p1.Y) * ((p1.X - p2.X) / (p1.Y - p2.Y)) * p1.X) < pt.X) { return 1; } } } } return 0; }).Sum(); if (numIntersections % 2 == 0) { return PointInPolygonLocation.Outside; } else { return PointInPolygonLocation.Inside; } } This function, PointInPolygon, takes the input Position, pt, iterates over the input sequence of position values, and uses the Jordan Curve method to determine how many times a ray extended from pt to the left intersects the polygon. The lambda expression will yield, into the "zipped" list, 1 for every segment that is crossed, and 0 for the rest. The sum of these values determines if pt is inside or outside of the polygon (odd == inside, even == outside). So far, so good. Now, for any consecutive pairs of position values in the sequence (i.e. in any execution of the lambda), we can also determine if pt is ON the segment p1, p2. If that is the case, we can stop the calculation because we have our answer. Ultimately, my question is this: Can I perform this calculation (maybe using Aggregate?) such that we will only iterate over the sequence no more than 1 time AND can we stop the iteration if we encounter a segment that pt is ON? In other words, if pt is ON the very first segment, there is no need to examine the rest of the segments because we have the answer. It might very well be that this operation (particularly the requirement/desire to possibly stop the iteration early) does not really lend itself well to the LINQ approach. It just occurred to me that maybe the lambda expression could yield a tuple, the intersection value (1 or 0 or maybe true or false) and the "on" value (true or false). Maybe then I could use TakeWhile(anontype.PointOnPolygon == false). If I Sum the tuples and if ON == 1, then the point is ON the polygon. Otherwise, the oddness or evenness of the sum of the other part of the tuple tells if the point is inside or outside.

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