Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

tpeqd: use numerically stable formula for computing the central angle from (phi_1, lam_1) to (phi_2, lam_2) (fixes #4008) #4009

Merged
merged 1 commit into from
Jan 22, 2024
Merged

tpeqd: use numerically stable formula for computing the central angle from (phi_1, lam_1) to (phi_2, lam_2) (fixes #4008) #4009

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
13 changes: 10 additions & 3 deletions src/projections/tpeqd.cpp
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -90,16 +90,23 @@ PJ *PJ_PROJECTION(tpeqd) {
Q->cs = Q->cp1 * Q->sp2;
Q->sc = Q->sp1 * Q->cp2;
Q->ccs = Q->cp1 * Q->cp2 * sin(Q->dlam2);
Q->z02 = aacos(P->ctx, Q->sp1 * Q->sp2 + Q->cp1 * Q->cp2 * cos(Q->dlam2));

const auto SQ = [](double x) { return x * x; };
// Numerically stable formula for computing the central angle from
// (phi_1, lam_1) to (phi_2, lam_2).
// Special case of Vincenty formula on the sphere.
// https://en.wikipedia.org/wiki/Great-circle_distance#Computational_formulae
const double cs_minus_sc_cos_dlam = Q->cs - Q->sc * cos(Q->dlam2);
Q->z02 = atan2(sqrt(SQ(Q->cp2 * sin(Q->dlam2)) + SQ(cs_minus_sc_cos_dlam)),
Q->sp1 * Q->sp2 + Q->cp1 * Q->cp2 * cos(Q->dlam2));
if (Q->z02 == 0.0) {
// Actually happens when both lat_1 = lat_2 and |lat_1| = 90
proj_log_error(P, _("Invalid value for lat_1 and lat_2: their absolute "
"value should be < 90°."));
return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);
}
Q->hz0 = .5 * Q->z02;
A12 = atan2(Q->cp2 * sin(Q->dlam2),
Q->cp1 * Q->sp2 - Q->sp1 * Q->cp2 * cos(Q->dlam2));
A12 = atan2(Q->cp2 * sin(Q->dlam2), cs_minus_sc_cos_dlam);
const double pp = aasin(P->ctx, Q->cp1 * sin(A12));
Q->ca = cos(pp);
Q->sa = sin(pp);
Expand Down
Loading