So far my process is as follows:
Markers are square markers of a known size, an example is below:
Detect markers
Get translation + rotation of markers relative to camera using POSIT - result is a transformation matrix of the matrix in camera coordinate space.
Now I am trying to find the distance in mm between the related corners of two markers. An example is below:
By distance I mean the euclidean distance (sqrt(x^2 + y^2 + z^2)).
I am thinking it should be possible as I have a reference for mm distance (the edge of any of the markers is a known mm distance), but I am unsure about how I would get to this from just the two transformation matrices I have.
EDIT:
I have managed so far to get the relative distance between the marker centers by multiplying the 2nd transform matrix by the inverse of the first and looking at the translation of the result.
I figured that I can get the plane of each marker by getting the normal and point. From there I should be able to get the 3d coord of a corner by looking at how the 2D point intersects that plane and from there the rest should be easy. I am not entirely sure how to get the normal of the marker and how to work out the point where the 2D coord representing the corner intersects the plane.
Extra info:
Using XNA and C#
Using AForge.net for video input and marker detection.
For calculation simplicity, I will suppose that the markers are on the XY plane. Otherwise, you would have to do some projections to get the camera position into the marker's plane.
Given the translation matrix, you should be able to define the camera position. We will try to find the absolute difference between those point's coordinate
Let's assume pC(xc,yc) the camera position, pA(xa,ya) the first marker position, pB(xb,yb) the second marker position.
lAC the absolute distance between A and the camera, which is known
lBC the absolute distance between B and the camera, which is known
lAB the absolute distance between B and A
dAC(dcax,dcay) the manhattan distance between the camera and A,
dBC(dcbx,dcby) and dAB(dabx,daby) likewise.
dcax = sqrt( lAC^2 - (xc-xa)^2)
dcay = sqrt( lAC^2 - (yc-ya)^2)
dcbx = sqrt( lBC^2 - (xc-xb)^2)
dcby = sqrt( lBC^2 - (yc-yb)^2)
dabx = abs(dcbx-dcax)
daby = abs(dcby-dcay)
lAB = sqrt(dabx^2 + daby^2)
Ps: It's been a long time since I've done this, Would appreciate a double check :)
Related
I want to calculate the perimeter of various irregular 3D objects, how can I do this in Unity 3D using C#?
My idea is:
Get a plane by inputting the coordinates of 3 points, then get the intersection of the plane and the object to be calculated, and then calculate the perimeter of the cumulative distance of these intersections.
But I have no idea to do this.
I don't think there is one answer for every 3D object, if you want to find the perimeter for a particular shape you have to find the formula for that.
In case of a sphere:
c is position of the plane.
c0 is position of the sphere.
p is distance between c and c0.
r = sqrt(R2 - p2).
Then the perimeter of the intersection is: 2rpi.
I have a 360 spherical video. I use this video as a texture on a sphere in Unity. Inside the sphere is a camera and this functions as the setup for my Virtual Reality experience. Pretty basic.
I am trying to write a bit of code on the web where people can upload 360 images and videos, place a marker/hotspot on the 360 spherical image/video, and then apply the image/video-texture on the sphere in Unity3D. If I overlay a simple x/y coordinate grid on the 360 video/image-texture, put in some x/y-coordinates to place the marker/hotspot, and put the texture back on the sphere, Unity will not interpret this correctly since we are now in 3D space and we are looking at the texture from within the sphere mapped onto the plane with all the distortion happening.
My question is, how do I convert these x and y coordinates on the 2D plane of the 360 video texture to coordinates that can be understood in 3D within Unity3D?
My first thought was to use 2-dimensional cartesian coordinates and convert these into spherical coordinates, but I seem to be missing a z-axis in the cartesian coordinates to make this work.
Is the z-axis simply 0 or is it the radius from center of the sphere to the x/y-coordinate? What does the z-axis represent? Is there maybe two coordinate systems. One that is coordinates on a plane and one that is from the centre of the sphere?
This is the conversion code that I have so far:
public static void CartesianToSpherical(Vector3 cartCoords, out float outRadius, out float outPolar, out float outElevation){
if (cartCoords.x == 0)
cartCoords.x = Mathf.Epsilon;
outRadius = Mathf.Sqrt((cartCoords.x * cartCoords.x)
+ (cartCoords.y * cartCoords.y)
+ (cartCoords.z * cartCoords.z));
outPolar = Mathf.Atan(cartCoords.z / cartCoords.x);
if (cartCoords.x < 0)
outPolar += Mathf.PI;
outElevation = Mathf.Asin(cartCoords.y / outRadius);
}
This is my very first post so please excuse me if I am doing anything wrong and let me know how to improve.
Spherical co-ordinates are different from 2d or 3d co-ordinates as you need to measure them in radians. It is usually measured from the center of the sphere and XY axis. It marks a rectangular area on the surface of the sphere. Please refer to this link for spherical co-ordinates in unity - https://blog.nobel-joergensen.com/2010/10/22/spherical-coordinates-in-unity/
I have two points specified as lat/long(s) and would like to insert a new point in between them a certain distance (in meters) from point the initial point.
Presumably I convert the lat/longs to radians and then use a version of midpoint formula?
How can i accomplish this task?
I'm living in c# land btw.
TIA
The exact solution is not that simple (an approximate solution is just given by linear interpolation). You're not going to love it.
The trajectory follows a great circle, which is the intersection between the sphere and a plane through the center and the two given points.
First convert from spherical to Cartesian coordinates. Then by the cross product of the vectors from the center to the two points, determine the direction of the normal to the plane (normalize the vector). Then use the formula for 3D rotation around this axis and rotate the starting point. The rotation angle is given by the desired distance divided by the radius of the Earth. Finally, convert back to spherical coordinates.
Although my current project is XNA, this question is about the basic mathematics of 3D to 2D mapping. In fact, and for the same reason, let's assume a WinForms graphics surface to draw on.
I have the following configuration:
Camera position of (x=0, y=0, z=0) and direction vector of (x=0, y=0, z=0).
A line segment in 3D with the following points: (10, 10, 10), (100, 100, 100).
I want to transform these coordinates and draw them on a 2D surface. So depending on the camera, the line segment should transform from (x1, y1, z1),(x2, y2, z2) to (x1, y1),(x2, y2).
I think you are looking for an orthogonal or perspective projection. There is a lot of information online if you search for it but here is the gist.
A camera looking at the origin, located a distance d along the z-axis will project a point at (x,y,z) onto a plane as:
// Orthogonal
planar_x = x
planar_y = y
// Perspective
planar_x = x*d/(d-z)
planar_y = y*d/(d-z)
Example
A point at (10,10,10) with the camera located a distance of 500 along the z axis will have planar coordinates (10*500/(500-10), 10*500/(500-10)) = (10.204, 10.204)
A point at (10,10,100) with the camera located a distance of 500 along the z axis will have planar coordinates (10*500/(500-100), 10*500/(500-100)) = (12.5, 12.5)
So the closer a shape is to the camera the larger it appears.
To transform the planar model coordinates to pixel coordinates I use the following scaling
scale = max_model_size/Math.Min(Height,Width);
pixel_x = Width/2 + x/scale;
pixel_y = Height/2- y/scale;
This is how I can use GDI to draw 3D shapes on a windows form.
Of course if you want to use OpenGL then look here for a similar question.
I have three Vector3 points in 3D space. I need to copy the rotation (the tangent?) of this triangle to the orientation of a 3D model. How can I calculate the triangles Vector3 tangent or create a rotation matrix out of those points?
Finding the angle of a triangle is described here: Find the normal angle of the face of a triangle in 3D, given the co-ordinates of its vertices
Suppose you find the normal and call it N'. It should be trivial for you to write the normal of the "unrotated" triangle, N, eg <1, 0, 0>. It should also be trivial to figure out how to rotate from N to N' and you can create a rotation matrix for it with Matrix.CreateFromAxisAngle in XNA. This matrix should rotate everything like you want.