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Window for selecting the screen size for the screen in 3D

I want to know the best algorithm to be able to scale in the field / window for selecting the screen space in 3D.

I am currently working, but it does not seem to scale correctly when the distance from the target is significant.

He is currently working by calculating the scale of the selection window relative to the width / height of the viewport and applying this scale to the distance / range of the camera to the target.

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2 answers

This is actually not so simple. Look at this image (this is a 2D projection for simplicity):

frustum1

- . , . , , . , .

​​ :

frustum2

, . , (fovy, znear, zfar, aspect), , .

:

:

h = 2 * tan(fovy/2) * znear
w = aspect * h

:

rectangle = ( x0, y0, x1, y1 )

- :

rcenter = ( (x0+x1)/2, (y0+y1)/2 )

:

frustum3

, , :

center = ( (rcenter.x / screen_width  - 0.5) * w,
           (0.5 - rcenter.y / screen_height) * h, 0 )

:

centerWS = center.x * camera_right_dir + center.y * camera_up_dir

(dir2n):

dir1 = camera_dir * znear
dir2 = dir1 + centerWS
dir2n = normalize(dir2)

(. 2):

, . , :

(w, h) / dist = (w * (x1-x0)/screen_width, h * (y1-y0)/screen_height) / znear
(1, 1) / dist = ( (x1-x0)/screen_width, (y1-y0)/screen_height) / znear
(1/dist, 1/dist) = ( (x1-x0)/screen_width, (y1-y0)/screen_height) / znear

:

dist = znear * screen_width / (x1-x0)

:

dist = znear * screen_height / (y1-y0)

, , , , (x1-x0) (y1-y0) .

:

pos2 = pos1 + dir2n * (dist-znear)
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, , , .

, , .

, . , :

:
H = tan(fovy/2) * nearPlane; -------- (1)

:

fraction = WindowHeight / rectangle height;  
h = H * fraction; ---------(2)

, . , D - , ,
h / nearPlane = H / (nearPlane+D) -------- (3)

(2), (3) :

fraction / nearPlane = 1 / (nearPlane+D)

D :

D = (nearPlane / fraction)  - nearPlane; 


D = nearPlane * (1-fraction)/fraction;

D., .

, .

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