Calculation in the Utils3D.projectVectors() method

The Utils3D.projectVectors() method projects a Vector of three-dimensional space coordinates to a Vector of two-dimensional space coordinates. And the method also sets the t value of the uvt data.

Values for the calculation in the Utils3D.projectVectors() method

The Utils3D.projectVectors() method calculates t value of the uvt data by the following formula:

t value = 1 / (Distance to the origin + z coordinate value)

Also, the method calculates projected x and y values by the following formula:

Projected x or y value = Three-dimensional space x or y coordinate * Focal length * t value

The frame action below compares the results of calculation by the formulas above with the methods’. And [Output] is as follows:

0,0,0.0004 // uvt data
0.0004 // Calculated t value
20,20 // Projected x and y coordinates
20 // Calculated two-dimensional space x or y coordinate

var myPerspective:PerspectiveProjection = new PerspectiveProjection();
var myMatrix3D:Matrix3D = new Matrix3D();
var nDistance:Number = 1000;  // Distance to the origin
var nX:Number = 100;  // Three-dimensional space x or y coordinate
var nZ:Number = 1500;  // Three-dimensional z coordinate
var vertices3D:Vector.<Number> = Vector.<Number>([nX, nX, nZ]);
var vertices2D:Vector.<Number> = new Vector.<Number>();
var uvtData:Vector.<Number> = Vector.<Number>([0, 0, 0]);
var nT:Number = 1/(nDistance + nZ);  // t value
myPerspective.focalLength = 500;  // Focal length 
myMatrix3D.appendTranslation(0, 0, nDistance);
myMatrix3D.append(myPerspective.toMatrix3D());
Utils3D.projectVectors(myMatrix3D, vertices3D, vertices2D, uvtData);
trace(uvtData);  // uvt data
trace(nT);  // Calculated t value
trace(vertices2D);  // Projected x and y coordinates
trace(nX * myPerspective.focalLength * nT);  // Calculated two-dimensional space x or y coordinate