algorithm - calculating point of intersection between far or near plane and a triangle -

suppose, near , far values of gluperspective 1 , 100 respectively. want clip portion of triangle having z values greater (-near) or less (-far) , divide remaining polygon 2 triangles following images.

considering far plane:

considering near plane:

another case:

i have calculated intersection points in following way: z_clip=-far (for considering far plane) or z_clip=-near (for considering near plane)

for example: f consider edge between (x1,y1,z1) , (x2,y2,z2), then:

co-efficient = (z_clip - z1) / (z2 - z1) xc = x1 + co-efficient * (x2 - x1) yc = y1 + co-efficient * (y2 - y1) zc = z_clip 

(xc,yc,zc) point of intersection. similarly, can calculate point of intersection other edge. example: edge between (10, 0, -50) , (0, 0, -150) cut in point (5, 0, -100).

original triangle:  0 0 -150 10 0 -50 0 10 -50  after clipping:  triangle1: 0 10 -50 5 0 100 0 5 -100  triangle2: 10 0 -50 0 5 -100 0 10 -50 

am right in calculation procedure or there wrong in procedure?