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rv:: more points in tricenter

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Zeno Rogue
2026-04-12 17:55:04 +02:00
parent 95160852c5
commit 28f208e51c
1 changed files with 69 additions and 23 deletions
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92
rogueviz/tricenter.cpp
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@@ -62,6 +62,15 @@ hyperpoint ortho1(hyperpoint A, hyperpoint B) {
return X;
}
hyperpoint mirror_line_point(hyperpoint A, hyperpoint B, hyperpoint X) {
if(1) {
simplifier s1(gpushxto0(A), {&A, &B, &X});
simplifier s2(spintox(B), {&A, &B, &X});
X[1] = -X[1];
}
return X;
}
hyperpoint linecross3(hyperpoint A, hyperpoint A1, hyperpoint B, hyperpoint B1, hyperpoint C, hyperpoint C1, const string& s) {
hyperpoint res = linecross(A, A1, B, B1);
println(hlog, s, is_on_line(C, C1, res) ? " verification: OK" : " verification: failed");
@@ -93,36 +102,73 @@ void tricenter() {
markpoint(C, 0xFF0000);
markseg(A, B, 0xFF0000FF); markseg(B, C, 0xFF0000FF); markseg(C, A, 0xFF0000FF);
/* hyperpoint A1 = bisector(A, B, C);
// indices as in: https://faculty.evansville.edu/ck6/encyclopedia/ETC.html
hyperpoint A1 = bisector(A, B, C);
hyperpoint B1 = bisector(B, C, A);
hyperpoint C1 = bisector(C, A, B);
hyperpoint D1 = linecross3(A, A1, B, B1, C, C1, "incenter");
hyperpoint D1 = linecross3(A, A1, B, B1, C, C1, "incenter"); ignore(D1);
markseg(A, A1, 0x00FF00FF); markseg(B, B1, 0x00FF00FF); markseg(C, C1, 0x00FF00FF);
markpoint(D1, 0x00FF00); */
markpoint(D1, 0x00FF00);
hyperpoint C2 = perpendicular_drop(A, B, C);
hyperpoint A2 = perpendicular_drop(B, C, A);
hyperpoint B2 = perpendicular_drop(C, A, B);
hyperpoint D2 = linecross3(A, A2, B, B2, C, C2, "orthocenter");
markseg(A, A2, 0xFFFF00FF); markseg(B, B2, 0xFFFF00FF); markseg(C, C2, 0xFFFF00FF);
markpoint(D2, 0xFFFF00);
hyperpoint C2 = mid(A, B);
hyperpoint A2 = mid(B, C);
hyperpoint B2 = mid(C, A);
hyperpoint D2 = linecross3(A2, A, B2, B, C2, C, "centroid");
markseg(A2, A, 0xFF00FFFF); markseg(B2, B, 0xFF00FFFF); markseg(C2, C, 0xFF00FFFF);
markpoint(D2, 0xFF00FF);
hyperpoint C3 = mid(A, B);
hyperpoint A3 = mid(B, C);
hyperpoint B3 = mid(C, A);
hyperpoint D3 = linecross3(A3, A, B3, B, C3, C, "centroid");
markseg(A3, A, 0xFF00FFFF); markseg(B3, B, 0xFF00FFFF); markseg(C3, C, 0xFF00FFFF);
markpoint(D3, 0xFF00FF);
/*
hyperpoint C3 = ortho1(C2, A);
hyperpoint A3 = ortho1(A2, B);
hyperpoint B3 = ortho1(B2, C);
hyperpoint D3 = linecross3(A2, A3, B2, B3, C2, C3, "circumcenter");
markseg(A2, A3, 0x00FFFFFF); markseg(B2, B3, 0x00FFFFFF); markseg(C2, C3, 0x00FFFFFF);
markpoint(D3, 0x00FFFF);
hyperpoint C4 = ortho1(C3, A);
hyperpoint A4 = ortho1(A3, B);
hyperpoint B4 = ortho1(B3, C);
hyperpoint D4 = linecross3(A3, A4, B3, B4, C3, C4, "circumcenter");
markseg(A3, A4, 0x00FFFFFF); markseg(B3, B4, 0x00FFFFFF); markseg(C3, C4, 0x00FFFFFF);
markpoint(D4, 0x00FFFF);
hyperpoint C4 = perpendicular_drop(A, B, C);
hyperpoint A4 = perpendicular_drop(B, C, A);
hyperpoint B4 = perpendicular_drop(C, A, B);
hyperpoint D4 = linecross3(A, A4, B, B4, C, C4, "orthocenter");
markseg(A, A4, 0xFFFF00FF); markseg(B, B4, 0xFFFF00FF); markseg(C, C4, 0xFFFF00FF);
markpoint(D4, 0xFFFF00);
auto markcc = [&] (hyperpoint h1, hyperpoint h2, hyperpoint h3, color_t col, const string& s) {
if(is_on_line(h1, h2, h3)) {
println(hlog, s, ": lie on a line");
if(h1[0] > h2[0]) swap(h1, h2);
if(h2[0] > h3[0]) swap(h3, h2);
if(h1[0] > h2[0]) swap(h1, h2);
markseg(h1, h3, col);
}
else {
hyperpoint ctr = circumscribe(h1, h2, h3);
ld rad = hdist(h1, ctr);
for(int i=0; i<=360; i++) curvepoint(xspinpush0(i*1._deg, rad));
queuecurve(S * rgpushxto0(ctr), col, 0, PPR::LINE);
}
};
markcc(D2, D3, D4, 0xFFFFFFFF, "Euler line");
// the nine-point circle center:
// - passes through the centers of the sides
hyperpoint D5_a = circumscribe(A2, B2, C2);
// - passes through the feet of the altitudes
hyperpoint D5_b = circumscribe(A4, B4, C4);
// - passes through the midpoints of AD4, BD4 and CD4
hyperpoint D5_c = circumscribe(mid(A, D4), mid(B, D4), mid(C, D4));
markpoint(D5_a, 0xC0C0C0);
markpoint(D5_b, 0xC0C0C0);
markpoint(D5_c, 0xC0C0C0); */
hyperpoint A6 = mirror_line_point(A, A1, A2);
hyperpoint B6 = mirror_line_point(B, B1, B2);
hyperpoint C6 = mirror_line_point(C, C1, C2);
hyperpoint D6 = linecross3(A, A6, B, B6, C, C6, "symmedian point");
markseg(A, A6, 0x8000FFFF); markseg(B, B6, 0x8000FFFF); markseg(C, C6, 0x8000FFFF);
markpoint(D6, 0x8000FF);
markseg(D3, D2, 0xFFFFFFFF); markseg(D3, D4, 0xFFFFFFFF); markseg(D2, D4, 0xFFFFFFFF);
if(is_on_line(D3, D2, D4)) println(hlog, "Euler line verified"); else println(hlog, "Euler line failed");
}
void enable() {