B(0;h;0)

C(0;0;h)

A(h;0;0)

P(x; y; z)

x

z

y

h

\frac{dx}{2}+\frac{dy}{2}+\frac{dz}{2}
=\frac{d}{2}(x+y+z)=\frac{dh}{2}.

x+y+z=h.

Sirgeid AB, BC ja CA
nimetame koordinaattelgedeks.

x=0

y=0

z=0

Saadud koordinaate, mis esitavad kolmnurga
punktide kaugusi kolmest sirgest, nimetame 
trilineaarseteks koordinaatideks.

Trilineaarsed koordinaadid

Joonestame kolmnurgad PBC, PAB ja PAC:

S_{PBC} + S_{PAB} + S_{PCA} = S_{ABC}.

B = (-1.7320508075688745, 1)
C = (6.06217782649107, -3.5)
A = (6.06217782649107, 5.5)
hulknurkABC, c, d, b = Polygon(A, B, C)
q = 0 (slider from 0 to 14, step 1)
P = PointIn(hulknurkABC)
P' = Mirror(P, c)
P'_1 = Mirror(P, d)
P'_2 = Mirror(P, b)
D = Midpoint(P, P'_1)
E = Midpoint(P, P')
F = Midpoint(P, P'_2)
a = Segment(P, D)
e = Segment(P, E)
f = Segment(P, F)
G = Intersect(c, d)
hulknurk1, c_1, g, p = Polygon(G, P, C)
hulknurk2, p_1, c_2, a_1 = Polygon(C, A, P)
hulknurk3, a_2, g_1, p_2 = Polygon(G, P, A)
h = OrthogonalLine(A, p)
H = Intersect(h, p)
I = Intersect(p_1, c_2)
i = Segment(I, H)