Because of the Moodle-STACK environment I am currently limited to JSXGraph 0.99.7. Is there a way to get the union of two curves given by coordinate vectors (polygons) in that version?
In 1.2.1 I do this using Clip.union(), which works fine in jsfiddle (not exactly a minimum working example) but not in STACK.
this.b = board.create('curve', JXG.Math.Clip.union( bneu, this.b, board),
{opacity: true, fillcolor:'lightgray', strokeWidth: normalStyle.strokeWidth,
strokeColor: normalStyle.strokeColor});
In 0.99.7 you have to do the union by hand. As long as the shapes are not overlapping this might be doable without too much work. Define a curve and set its
updataDataArray method:
c = board.create('curve', [[], []]);
c.updateDataArray = function() {
this.dataX = [];
this.dataY = [];
// copy now the coordinates of the polygons / curves into
// these arrays.
};
board.update();
You can access the coordinates of the polygon vertices by
polygon.vertices[i].X();
polygon.vertices[i].Y();
Attention: the last vertex is a copy of the first vertex, to make the polygon a closed curve.
The coordinates of a curve can be accessed by
curve.points[i].usrCoords[1]; // x-coordinate
curve.points[i].usrCoords[2]; // y-coordinate
The curve path can be interrupted by adding NaNs:
this.dataX.push(NaN);
this.dataY.push(NaN);
Hope that helps a little bit.
Related
Openlayers provides useful functions for drawing boxes and rectangles and also has ol.geom.Geometry.prototype.rotate(angle, anchor) for rotating a geometry around a certain anchor. Is it possible to lock the rotation of a box/rectangle while modifying it?
Using the OpenLayers example located here to draw a box with a certain rotation to illustrate the point:
I would like the box/rectangle to maintain its rotation while still being able to drag the sides longer and shorter. Is there a simple way to achieve this?
Answering with the solution I came up with.
First of all, add the feature(s) to a ModifyInteraction so you are able to modify by dragging the corners of the feature.
this.modifyInteraction = new Modify({
deleteCondition: eventsCondition.never,
features: this.drawInteraction.features,
insertVertexCondition: eventsCondition.never,
});
this.map.addInteraction(this.modifyInteraction);
Also, add event handlers upon the events "modifystart" and "modifyend".
this.modifyInteraction.on("modifystart", this.modifyStartFunction);
this.modifyInteraction.on("modifyend", this.modifyEndFunction);
The functions for "modifystart" and "modifyend" look like this.
private modifyStartFunction(event) {
const features = event.features;
const feature = features.getArray()[0];
this.featureAtModifyStart = feature.clone();
this.draggedCornerAtModifyStart = "";
feature.on("change", this.changeFeatureFunction);
}
private modifyEndFunction(event) {
const features = event.features;
const feature = features.getArray()[0];
feature.un("change", this.changeFeatureFunction);
// removing and adding feature to force reindexing
// of feature's snappable edges in OpenLayers
this.drawInteraction.features.clear();
this.drawInteraction.features.push(feature);
this.dispatchRettighetModifyEvent(feature);
}
The changeFeatureFunction is below. This function is called for every single change which is done to the geometry as long as the user is still modifying/dragging one of the corners. Inside this function, I made another function to adjust the modified rectangle into a rectangle again. This "Rectanglify"-function moves the corners which are adjacent to the corner which was just moved by the user.
private changeFeatureFunction(event) {
let feature = event.target;
let geometry = feature.getGeometry();
// Removing change event temporarily to avoid infinite recursion
feature.un("change", this.changeFeatureFunction);
this.rectanglifyModifiedGeometry(geometry);
// Reenabling change event
feature.on("change", this.changeFeatureFunction);
}
Without going into too much detail, the rectanglify-function needs to
find rotation of geometry in radians
inversely rotate with radians * -1 (e.g. geometry.rotate(radians * (-1), anchor) )
update neighboring corners of the dragged corner (easier to do when we have a rectangle which is parallel to the x and y axes)
rotate back with the rotation we found in 1
--
In order to get the rotation of the rectangle, we can do this:
export function getRadiansFromRectangle(feature: Feature): number {
const coords = getCoordinates(feature);
const point1 = coords[0];
const point2 = coords[1];
const deltaY = (point2[1] as number) - (point1[1] as number);
const deltaX = (point2[0] as number) - (point1[0] as number);
return Math.atan2(deltaY, deltaX);
}
In reference to this question
Drawing a line between two points using SceneKit
I'm drawing a line in 3D and want to make it thicker by using this code
func renderer(aRenderer: SCNSceneRenderer, willRenderScene scene: SCNScene, atTime time: NSTimeInterval) {
//Makes the lines thicker
glLineWidth(20)
}
but it doesn't work, iOS 8.2.
Is there another way?
Update
From the docs
https://developer.apple.com/library/prerelease/ios/documentation/SceneKit/Reference/SCNSceneRendererDelegate_Protocol/index.html#//apple_ref/occ/intfm/SCNSceneRendererDelegate/renderer:updateAtTime:
I did add SCNSceneRendererDelegate and a valid line width but still could not get the line width to increase.
You cannot assign any number to glLineWidth().
You can check the range of possible values of glLineWidth()by:
glGetFloatv(GL_LINE_WIDTH_RANGE,sizes);
One crazy idea is to use a cylinder for drawing lines ;). I use it when I want to have nice and controllable lines but I am not aware of a handy OpenGl function to do so.
#G Alexander: here you go my implementation of cylinder. It is a bit tedious but it is what I have at the moment.
If you give me points p0 and p1, Vector normal=(p1-p0).normalize() would be the axis of the cylinder.
pick point p2 that is not on the vector Normal.
q=(p2-p0).normalize();
normal.crossproduct(q)=v0;
normal.crossproduct(v0)=v1;
Having these two vectors you can have circles with any radius that are stacked along the axis of the cylinder using the following function (A cylinder is a stack of circles):
public Circle make_circle(Point center, Vector v0, Vector v1, double radius)
{
Circle c;
for (double i = 0; i < 2 * Math.PI; i += 0.05)
{
Point p = new Point(center + radius * Math.Cos(i) * v0 + radius * Math.Sin(i) * v1);
c.Add(p);
}
return c;
}
You only need to make circles using this function along the axis of the cylinder:
List<Circle> Cylinder = new List<Circle>();
for(double i=0;i<1;i+=0.1)
{
Cylinder.add( make_circle(P0+i*normal, v0, v1,radius);
}
Now you should take two consecutive circles and connect them with quads by sampling uniformly.
I have implemented it this way since I had circles implemented already.
A simpler way to implement is make the circle along the x axis and then rotate and translate it to p0 and make it align with normal or to use gluCylinder if you are the fan of Glu....
Hopefully it works for you.
I am currently using a Project Tango tablet for robotic obstacle avoidance. I want to create a matrix of z-values as they would appear on the Tango screen, so that I can use OpenCV to process the matrix. When I say z-values, I mean the distance each point is from the Tango. However, I don't know how to extract the z-values from the TangoXyzIjData and organize the values into a matrix. This is the code I have so far:
public void action(TangoPoseData poseData, TangoXyzIjData depthData) {
byte[] buffer = new byte[depthData.xyzCount * 3 * 4];
FileInputStream fileStream = new FileInputStream(
depthData.xyzParcelFileDescriptor.getFileDescriptor());
try {
fileStream.read(buffer, depthData.xyzParcelFileDescriptorOffset, buffer.length);
fileStream.close();
} catch (IOException e) {
e.printStackTrace();
}
Mat m = new Mat(depthData.ijRows, depthData.ijCols, CvType.CV_8UC1);
m.put(0, 0, buffer);
}
Does anyone know how to do this? I would really appreciate help.
The short answer is it can't be done, at least not simply. The XYZij struct in the Tango API does not work completely yet. There is no "ij" data. Your retrieval of buffer will work as you have it coded. The contents are a set of X, Y, Z values for measured depth points, roughly 10000+ each callback. Each X, Y, and Z value is of type float, so not CV_8UC1. The problem is that the points are not ordered in any way, so they do not correspond to an "image" or xy raster. They are a random list of depth points. There are ways to get them into some xy order, but it is not straightforward. I have done both of these:
render them to an image, with the depth encoded as color, and pull out the image as pixels
use the model/view/perspective from OpenGL and multiply out the locations of each point and then figure out their screen space location (like OpenGL would during rendering). Sort the points by their xy screen space. Instead of the calculated screen-space depth just keep the Z value from the original buffer.
or
wait until (if) the XYZij struct is fixed so that it returns ij values.
I too wish to use Tango for object avoidance for robotics. I've had some success by simplifying the use case to be only interested in the distance of any object located at the center view of the Tango device.
In Java:
private Double centerCoordinateMax = 0.020;
private TangoXyzIjData xyzIjData;
final FloatBuffer xyz = xyzIjData.xyz;
double cumulativeZ = 0.0;
int numberOfPoints = 0;
for (int i = 0; i < xyzIjData.xyzCount; i += 3) {
float x = xyz.get(i);
float y = xyz.get(i + 1);
if (Math.abs(x) < centerCoordinateMax &&
Math.abs(y) < centerCoordinateMax) {
float z = xyz.get(i + 2);
cumulativeZ += z;
numberOfPoints++;
}
}
Double distanceInMeters;
if (numberOfPoints > 0) {
distanceInMeters = cumulativeZ / numberOfPoints;
} else {
distanceInMeters = null;
}
Said simply this code is taking the average distance of a small square located at the origin of x and y axes.
centerCoordinateMax = 0.020 was determined to work based on observation and testing. The square typically contains 50 points in ideal conditions and fewer when held close to the floor.
I've tested this using version 2 of my tango-caminada application and the depth measuring seems quite accurate. Standing 1/2 meter from a doorway I slid towards the open door and the distance changed form 0.5 meters to 2.5 meters which is the wall at the end of the hallway.
Simulating a robot being navigated I moved the device towards a trash can in the path until 0.5 meters separation and then rotated left until the distance was more than 0.5 meters and proceeded forward. An oversimplified simulation, but the basis for object avoidance using Tango depth perception.
You can do this by using camera intrinsics to convert XY coordinates to normalized values -- see this post - Google Tango: Aligning Depth and Color Frames - it's talking about texture coordinates but it's exactly the same problem
Once normalized, move to screen space x[1280,720] and then the Z coordinate can be used to generate a pixel value for openCV to chew on. You'll need to decide how to color pixels that don't correspond to depth points on your own, and advisedly, before you use the depth information to further colorize pixels.
The main thing is to remember that the raw coordinates returned are already using the basis vectors you want, i.e. you do not want the pose attitude or location
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I need the ability to verify that a user has drawn a shape correctly, starting with simple shapes like circle, triangle and more advanced shapes like the letter A.
I need to be able to calculate correctness in real time, for example if the user is supposed to draw a circle but is drawing a rectangle, my hope is to be able to detect that while the drawing takes place.
There are a few different approaches to shape recognition, unfortunately I don't have the experience or time to try them all and see what works.
Which approach would you recommend for this specific task?
Your help is appreciated.
We may define "recognition" as the ability to detect features/characteristics in elements and compare them with features of known elements seen in our experience. Objects with similar features probably are similar objects. The higher the amount and complexity of the features, the greater is our power to discriminate similar objects.
In the case of shapes, we can use their geometric properties such as number of angles, the angles values, number of sides, sides sizes and so forth. Therefore, in order to accomplish your task you should employ image processing algorithms to extract such features from the drawings.
Below I present a very simple approach that shows this concept in practice. We gonna recognize different shapes using the numbers of corners. As I said: "The higher the amount and complexity of the features, the greater is our power to discriminate similar objects". Since we are using just one feature, the number of corners, we can differentiate a few different kinds of shapes. Shapes with the same number of corners will not be discriminated. Therefore, in order to improve the approach you might add new features.
UPDATE:
In order to accomplish this task in real time you might extract the features in real time. If the object to be drawn is a triangle and the user is drawing the fourth side of any other figure, you know that he or she is not drawing a triangle. About the level of correctness you might calculate the distance between the feature vector of the desired object and the drawn one.
Input:
The Algorithm
Scale down the input image since the desired features can ben detected in lower resolution.
Segment each object to be processed independently.
For each object, extract its features, in this case, just the number of corners.
Using the features, classify the object shape.
The Software:
The software presented below was developed in Java and using Marvin Image Processing Framework. However, you might use any programming language and tools.
import static marvin.MarvinPluginCollection.floodfillSegmentation;
import static marvin.MarvinPluginCollection.moravec;
import static marvin.MarvinPluginCollection.scale;
public class ShapesExample {
public ShapesExample(){
// Scale down the image since the desired features can be extracted
// in a lower resolution.
MarvinImage image = MarvinImageIO.loadImage("./res/shapes.png");
scale(image.clone(), image, 269);
// segment each object
MarvinSegment[] objs = floodfillSegmentation(image);
MarvinSegment seg;
// For each object...
// Skip position 0 which is just the background
for(int i=1; i<objs.length; i++){
seg = objs[i];
MarvinImage imgSeg = image.subimage(seg.x1-5, seg.y1-5, seg.width+10, seg.height+10);
MarvinAttributes output = new MarvinAttributes();
output = moravec(imgSeg, null, 18, 1000000);
System.out.println("figure "+(i-1)+":" + getShapeName(getNumberOfCorners(output)));
}
}
public String getShapeName(int corners){
switch(corners){
case 3: return "Triangle";
case 4: return "Rectangle";
case 5: return "Pentagon";
}
return null;
}
private static int getNumberOfCorners(MarvinAttributes attr){
int[][] cornernessMap = (int[][]) attr.get("cornernessMap");
int corners=0;
List<Point> points = new ArrayList<Point>();
for(int x=0; x<cornernessMap.length; x++){
for(int y=0; y<cornernessMap[0].length; y++){
// Is it a corner?
if(cornernessMap[x][y] > 0){
// This part of the algorithm avoid inexistent corners
// detected almost in the same position due to noise.
Point newPoint = new Point(x,y);
if(points.size() == 0){
points.add(newPoint); corners++;
}else {
boolean valid=true;
for(Point p:points){
if(newPoint.distance(p) < 10){
valid=false;
}
}
if(valid){
points.add(newPoint); corners++;
}
}
}
}
}
return corners;
}
public static void main(String[] args) {
new ShapesExample();
}
}
The software output:
figure 0:Rectangle
figure 1:Triangle
figure 2:Pentagon
The other way is you can use math with this problem using the average of each point that are smallest distance from the one your'e comparing it from,
first you must resize shape with the ones in your library of shapes and then:
function shortestDistanceSum( subject, test_subject ) {
var sum = 0;
operate( subject, function( shape ){
var smallest_distance = 9999;
operate( test_subject, function( test_shape ){
var distance = dist( shape.x, shape.y, test_shape.x, test_shape.y );
smallest_distance = Math.min( smallest_distance, distance );
});
sum += smallest_distance;
});
var average = sum/subject.length;
return average;
}
function operate( array, callback ) {
$.each(array, function(){
callback( this );
});
}
function dist( x, y, x1, y1 ) {
return Math.sqrt( Math.pow( x1 - x, 2) + Math.pow( y1 - y, 2) );
}
var square_shape = Array; // collection of vertices in a square shape
var triangle_shape = Array; // collection of vertices in a triangle
var unknown_shape = Array; // collection of vertices in the shape your'e comparing from
square_sum = shortestDistanceSum( square_shape, unknown_shape );
triangle_sum = shortestDistanceSum( triangle_shape, unknown_shape );
Where the lowest sum is the closest shape.
You have two inputs - the initial image and the user input - and you are looking for a boolean outcome.
Ideally you would convert all your input data to a comparable format. Instead, you could also parameterize both types of input and use a supervised machine learning algorithm (Nearest Neighbor comes to mind for closed shapes).
The trick is in finding the right parameters. If your input is a flat image file, this could be a binary conversion. If user input is a swiping motion or pen stroke, I'm sure there are ways to capture and map this as binary but the algorithm would probably be more robust if it used data closest to the original input.
Can anyone please help.
I have a cube which I have made in 3DS Max. I don't know the dimensions of the cube. Is there a way to get the vertices of each of the triangles of the faces of the cube? I am trying to get the normal to one of the faces of the cube to determine which way its pointing. So if I can determine the vertices I can get the normal for the face if I have 3 vertices, V1, V2 and V3, ordered in counterclockwise order, I can obtain the direction of the normal by computing (V2 - V1) x (V3 - V1), where x is the cross product of the two vectors.
I have looked in my models .fbx file and I can see a number of values there:
Vertices: *24 {
a: -15,-12.5,0,15,-12.5,0,-15,12.5,0,15,12.5,0,-15,-12.5,0.5,15,-12.5,0.5,-15,12.5,0.5,15,12.5,0.5}
PolygonVertexIndex: *36 {
a: 0,2,-4,3,1,-1,4,5,-8,7,6,-5,0,1,-6,5,4,-1,1,3,-8,7,5,-2,3,2,-7,6,7,-4,2,0,-5,4,6,-3}
Are these my models vertices?
Also, I would assume that Vertices: * 24 would be my list of vertices, but why is there only 24? Should a cube not have 36 vertices? And finally, if the coordinates for my vertices are PolygonVertexIndex: * 36 these values just seem off to me when I imagine the cube in my head with those dimensions?
Or alternatively, is there a automatic way to get the vertices of a cube without having to manually enter all the values for each vertex? I might have a couple of models to
Any help would be greatly appreciated
I can't figure why you need that... because when you load a model it is calculated , internally each vertex will have the normal,...
Anyway it is easy to calc...
The three first indexes define the first triangle of a face, the next three, the other triangle of a face.
You need only one triangle to calculate the normal...
So with the three indexes access to the veretex array and get three points... A, B and C
Now your normal is the result of the cross product between two vectors formed with that vertex.
Vector3 Normal = Vector3.Cross(B-A, C-B);
If the normal go back or forward will depend on the A,B,C order, can be CounterClockWise or ClockWise, but every triangle of the model will be ordered in one way. So you will have try it and fix it
You can write an XNA program which reads your normals without much hassle.
If you still want to calculate them, however, use this C# code, taken from FFWD, as a guide. Check the URL for a more detailed discussion on pros and cons. Personally, I'm not too happy with the result, but for the time being it works. Of course, since this code is FFWD related (implementation of Unity's API for XNA), it does not match XNA exactly, but the mathematics remain the same.
/// <summary>
/// Recalculates the normals.
/// Implementation adapted from http://devmaster.net/forums/topic/1065-calculating-normals-of-a-mesh/
/// </summary>
public void RecalculateNormals()
{
Vector3[] newNormals = new Vector3[_vertices.Length];
// _triangles is a list of vertex indices,
// with each triplet referencing the three vertices of the corresponding triangle
for (int i = 0; i < _triangles.Length; i = i + 3)
{
Vector3[] v = new Vector3[]
{
_vertices[_triangles[i]],
_vertices[_triangles[i + 1]],
_vertices[_triangles[i + 2]]
};
Vector3 normal = Vector3.Cross(v[1] - v[0], v[2] - v[0]);
for (int j = 0; j < 3; ++j)
{
Vector3 a = v[(j+1) % 3] - v[j];
Vector3 b = v[(j+2) % 3] - v[j];
float weight = (float)Math.Acos(Vector3.Dot(a, b) / (a.magnitude * b.magnitude));
newNormals[_triangles[i + j]] += weight * normal;
}
}
foreach (Vector3 normal in newNormals)
{
normal.Normalize();
}
normals = newNormals;
}