Databases
StackOverflow2013
Postsdbo
POReturn CATransform3D to map quadrilateral to quadrilateral
 

Note that there are some explanatory texts on larger screens.

plurals
  1. POReturn CATransform3D to map quadrilateral to quadrilateral
    primarykey
    data
    text
    <p>I'm trying to derive a CATransform3D that will map a quad with 4 corner points to another quad with 4 new corner points. I've spent a little bit of time researching this and it seems the steps involve converting the original Quad to a Square, and then converting that Square to the new Quad. My methods look like this (code borrowed from <a href="http://code.google.com/p/wiimotetuio/source/browse/trunk/WiimoteTUIO/Warper.cs" rel="noreferrer">here</a>):</p> <pre><code>- (CATransform3D)quadFromSquare_x0:(float)x0 y0:(float)y0 x1:(float)x1 y1:(float)y1 x2:(float)x2 y2:(float)y2 x3:(float)x3 y3:(float)y3 { float dx1 = x1 - x2, dy1 = y1 - y2; float dx2 = x3 - x2, dy2 = y3 - y2; float sx = x0 - x1 + x2 - x3; float sy = y0 - y1 + y2 - y3; float g = (sx * dy2 - dx2 * sy) / (dx1 * dy2 - dx2 * dy1); float h = (dx1 * sy - sx * dy1) / (dx1 * dy2 - dx2 * dy1); float a = x1 - x0 + g * x1; float b = x3 - x0 + h * x3; float c = x0; float d = y1 - y0 + g * y1; float e = y3 - y0 + h * y3; float f = y0; CATransform3D mat; mat.m11 = a; mat.m12 = b; mat.m13 = 0; mat.m14 = c; mat.m21 = d; mat.m22 = e; mat.m23 = 0; mat.m24 = f; mat.m31 = 0; mat.m32 = 0; mat.m33 = 1; mat.m34 = 0; mat.m41 = g; mat.m42 = h; mat.m43 = 0; mat.m44 = 1; return mat; } - (CATransform3D)squareFromQuad_x0:(float)x0 y0:(float)y0 x1:(float)x1 y1:(float)y1 x2:(float)x2 y2:(float)y2 x3:(float)x3 y3:(float)y3 { CATransform3D mat = [self quadFromSquare_x0:x0 y0:y0 x1:x1 y1:y1 x2:x2 y2:y2 x3:x3 y3:y3]; // invert through adjoint float a = mat.m11, d = mat.m21, /* ignore */ g = mat.m41; float b = mat.m12, e = mat.m22, /* 3rd col*/ h = mat.m42; /* ignore 3rd row */ float c = mat.m14, f = mat.m24; float A = e - f * h; float B = c * h - b; float C = b * f - c * e; float D = f * g - d; float E = a - c * g; float F = c * d - a * f; float G = d * h - e * g; float H = b * g - a * h; float I = a * e - b * d; // Probably unnecessary since 'I' is also scaled by the determinant, // and 'I' scales the homogeneous coordinate, which, in turn, // scales the X,Y coordinates. // Determinant = a * (e - f * h) + b * (f * g - d) + c * (d * h - e * g); float idet = 1.0f / (a * A + b * D + c * G); mat.m11 = A * idet; mat.m21 = D * idet; mat.m31 = 0; mat.m41 = G * idet; mat.m12 = B * idet; mat.m22 = E * idet; mat.m32 = 0; mat.m42 = H * idet; mat.m13 = 0 ; mat.m23 = 0 ; mat.m33 = 1; mat.m43 = 0 ; mat.m14 = C * idet; mat.m24 = F * idet; mat.m34 = 0; mat.m44 = I * idet; return mat; } </code></pre> <p>After calculating both matrices, multiplying them together, and assigning to the view in question, I end up with a transformed view, but it is wildly incorrect. In fact, it seems to be sheared like a parallelogram no matter what I do. What am I missing?</p> <p><strong>UPDATE 2/1/12</strong></p> <p>It seems the reason I'm running into issues may be that I need to accommodate for FOV and focal length into the model view matrix (which is the only matrix I can alter directly in Quartz.) I'm not having any luck finding documentation online on how to calculate the proper matrix, though.</p>
    singulars
    1. PO
      singulars
      1. PTAnswer
    1. This table or related slice is empty.
    1. PTQuestion
    1. USsevenflow
    1. USsevenflow
    plurals
    1. PL
      singulars
      1. LTLinked
    1. PL
      singulars
      1. LTLinked
    2. PL
      singulars
      1. LTLinked
    3. PL
      singulars
      1. LTLinked
    1. This table or related slice is empty.
    1. PO
      singulars
      1. PTAnswer
    1. VO
      singulars
      1. POReturn CATransform3D to map quadrilateral to quadrilateral
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. POReturn CATransform3D to map quadrilateral to quadrilateral
      1. USsevenflow
      1. VTBountyStart
    3. VO
      singulars
      1. POReturn CATransform3D to map quadrilateral to quadrilateral
      1. This table or related slice is empty.
      1. VTUpMod
    1. COUpdate: I've tried porting a few algorithms now and end up with a parallelogram every single time. There's got to be something I'm forgetting, but I'm at a loss.
      singulars
      1. POReturn CATransform3D to map quadrilateral to quadrilateral
      1. USsevenflow
    2. COHere is an other way to achieve this: http://stackoverflow.com/questions/9470493/transforming-a-rectangle-image-into-a-quadrilateral-using-a-catransform3d Let me know if this helps.
      singulars
      1. POReturn CATransform3D to map quadrilateral to quadrilateral
      1. USMonsieurDart
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload