Motion tracking question

[Buba Kastorski]

is it possible to track corner pin outside of the frame, or I have to shoot wide and crop in post?
for example : in the video #1 I hold a photo frame in my hands and the video #2 is playing inside of that frame,
when the tracking points are within the video #1 all is perfect, but when I move the photo frame outside of the video #1 I can't move the tracking points beyond the video #1 frame,
is there any solution?
thanks!

[Cole McDonald]

I was thinking about this the other day. So much corner pinning seems to ignore the fact that you can track a right triangle in space and extrapolate the 4th corner of a quadrangle described opposite the hypotenuse.

I just can't quite get of the freaking equation to type into the the invisible 4th point to make it stay locked to the other 3 points...grumble, stupid time passing since my last higher end math class.

Given a quadrangle ABCD, can any one come up with an equation for the cartesian coordinates of D given ABC describes a right triangle better than what I'm about to stab at?

My thoughts are:

B-A = delta AB = X1 (length of Segment AB, my programmer history comes out with variable choice here :) )
C-A = delta AC= Y1 (length of Segment AC)

Lower case letter will describe the Axis being considered

Dx = Cx + X1
Dy = By + Y1

The parts that confuse me are all the trig that will account for the expansion/contraction of the segments to account for an angular relationship to the camera... We have to assume that the center of the frame is considered the point of interest when figuring these out. This is the part that confuses me. I would assume we need to find a way to determine a Z relationship between the point of interest and A, B, C and D.

I open the mathematical floor! Have at.

[Bill Ravens]

In any right triangle:
a^2+b^2=c^2 where c=hypotenuse
and
sin x=a/c
cos x= b/c
tan x= a/b
where x=angle opposite "a"
and
x+y+90=180

This will sufficiently define the fourth point as a unique value.

[Buba Kastorski]

it's doable, I adjusted all points manually, not in the motion tracking, but in the properties of the video #2, hit U, you got all the corners position, frame by frame using position sliders,
thank god it's less than two seconds I needed to correct,
thanks!

[Cole McDonald]

By hand is a PITA, but I'm glad that worked for you.

Originally Posted by Bill Ravens

In any right triangle:
a^2+b^2=c^2 where c=hypotenuse
and
sin x=a/c
cos x= b/c
tan x= a/b
where x=angle opposite "a"
and
x+y+90=180

This will sufficiently define the fourth point as a unique value.

So long as we have a quadrangle whose center is in center frame and whose plane is parallel to the plane of the lens. If we define a Z coefficient based on the distance from center of frame that should allow us to determine how much extra travel the point has if the camera moves. (I have a specific shot I've been trying to figure this out for - and learn using expressions in Shake at the same time, slow going)