diff --git a/frontend/js/labs/geometry.js b/frontend/js/labs/geometry.js
index fe10e6a..0272fff 100644
--- a/frontend/js/labs/geometry.js
+++ b/frontend/js/labs/geometry.js
@@ -92,6 +92,13 @@ function gAngleDeg(A, B, C) {
return Math.acos(Math.max(-1, Math.min(1, cos))) * 180 / Math.PI;
}
+/** Ортоцентр треугольника ABC */
+function gOrthocenter(A, B, C) {
+ const Ha = gFoot(A, B, C); // основание высоты из A на BC
+ const Hb = gFoot(B, A, C); // основание высоты из B на AC
+ return gIntersectLines(A, Ha, B, Hb);
+}
+
/** Площадь многоугольника (формула Гаусса) */
function gPolygonArea(pts) {
let area = 0;
@@ -195,8 +202,11 @@ class GeoEngine {
return obj.centerId === id || obj.edgeId === id;
case 'point':
if (!obj.derived) return false;
- if (obj.constr === 'midpoint') return obj.srcA === id || obj.srcB === id;
- if (obj.constr === 'intersect') return obj.src1 === id || obj.src2 === id;
+ if (obj.constr === 'midpoint') return obj.srcA === id || obj.srcB === id;
+ if (obj.constr === 'intersect') return obj.src1 === id || obj.src2 === id;
+ if (obj.constr === 'centroid' || obj.constr === 'orthocenter')
+ return obj.ptA === id || obj.ptB === id || obj.ptC === id;
+ if (obj.constr === 'altitude_foot') return obj.ptA === id || obj.ptB === id || obj.ptC === id;
if (obj.constr === 'foot' || obj.constr === 'reflect') {
if (obj.srcPt === id || obj.srcLine === id) return true;
// Если srcLine — обычная прямая, зависим и от её точек
@@ -280,6 +290,25 @@ class GeoEngine {
obj.x = pP.x + (pB.x - pA.x);
obj.y = pP.y + (pB.y - pA.y);
}
+ } else if (obj.constr === 'centroid') {
+ const pA = _g(obj.ptA), pB = _g(obj.ptB), pC = _g(obj.ptC);
+ if (pA && pB && pC) {
+ obj.x = (pA.x + pB.x + pC.x) / 3;
+ obj.y = (pA.y + pB.y + pC.y) / 3;
+ }
+ } else if (obj.constr === 'orthocenter') {
+ const pA = _g(obj.ptA), pB = _g(obj.ptB), pC = _g(obj.ptC);
+ if (pA && pB && pC) {
+ const h = gOrthocenter(pA, pB, pC);
+ if (h) { obj.x = h.x; obj.y = h.y; obj.valid = true; }
+ else { obj.valid = false; }
+ }
+ } else if (obj.constr === 'altitude_foot') {
+ const pA = _g(obj.ptA), pB = _g(obj.ptB), pC = _g(obj.ptC);
+ if (pA && pB && pC) {
+ const f = gFoot(pA, pB, pC);
+ obj.x = f.x; obj.y = f.y;
+ }
}
} else if (obj.type === 'circle' && obj.derived) {
const pA = _g(obj.ptA), pB = _g(obj.ptB), pC = _g(obj.ptC);
@@ -733,9 +762,33 @@ class GeoSim {
if (obj.style?.dash) ctx.setLineDash(obj.style.dash);
ctx.beginPath(); ctx.moveTo(p1.x, p1.y); ctx.lineTo(p2.x, p2.y); ctx.stroke();
ctx.restore();
+ if (obj.tickMark) this._drawTickMark(ctx, p1, p2, obj.tickMark, col);
if (this.showLabels && obj.label) this._drawObjLabel(ctx, obj.label, {x:(p1.x+p2.x)/2, y:(p1.y+p2.y)/2}, col);
}
+ /* Метки равных сторон (штрихи поперёк отрезка) */
+ _drawTickMark(ctx, p1, p2, count, col) {
+ const dx = p2.x - p1.x, dy = p2.y - p1.y;
+ const len = Math.hypot(dx, dy);
+ if (len < 1e-9 || !count) return;
+ const ux = dx / len, uy = dy / len; // вдоль отрезка
+ const nx = -uy, ny = ux; // перпендикуляр
+ const TICK = 7, SPACING = 5;
+ const mx = (p1.x + p2.x) / 2, my = (p1.y + p2.y) / 2;
+ ctx.save();
+ ctx.strokeStyle = col; ctx.lineWidth = 2; ctx.globalAlpha = 0.9;
+ ctx.shadowColor = col; ctx.shadowBlur = 3;
+ for (let k = 0; k < count; k++) {
+ const off = (k - (count - 1) / 2) * SPACING;
+ const cx = mx + ux * off, cy = my + uy * off;
+ ctx.beginPath();
+ ctx.moveTo(cx + nx * TICK, cy + ny * TICK);
+ ctx.lineTo(cx - nx * TICK, cy - ny * TICK);
+ ctx.stroke();
+ }
+ ctx.restore();
+ }
+
_drawLine(ctx, obj) {
const m1 = this._mpt(obj.p1Id), m2 = this._mpt(obj.p2Id);
if (!m1 || !m2) return;
@@ -924,6 +977,13 @@ class GeoSim {
for (let i = 1; i < pts.length; i++) ctx.lineTo(pts[i].x, pts[i].y);
ctx.closePath(); ctx.stroke();
ctx.restore();
+ // Метки равных сторон
+ if (obj.sideMarks) {
+ for (let i = 0; i < pts.length; i++) {
+ const mark = obj.sideMarks[i] || 0;
+ if (mark > 0) this._drawTickMark(ctx, pts[i], pts[(i+1)%pts.length], mark, col);
+ }
+ }
}
_drawCircle(ctx, obj) {
@@ -1037,7 +1097,18 @@ class GeoSim {
ctx.strokeStyle = col;
ctx.lineWidth = 1.5;
- if (Math.abs(angle - 90) < 2) {
+ const explicitMark = poly.angleMarks?.[i] || 0; // 0=auto, 1-3=явный
+ if (explicitMark > 0 && bisLen > 1e-6) {
+ // Явные метки: 1-3 концентрические дуги
+ const midAngle = Math.atan2(bisY, bisX);
+ const halfSpread = Math.acos(Math.max(-1, Math.min(1, uAx*uCx + uAy*uCy))) / 2;
+ ctx.globalAlpha = 0.7;
+ for (let k = 0; k < explicitMark; k++) {
+ ctx.beginPath();
+ ctx.arc(Bpx.x, Bpx.y, ARC_R + k * 7, midAngle - halfSpread, midAngle + halfSpread, false);
+ ctx.stroke();
+ }
+ } else if (Math.abs(angle - 90) < 2) {
// Прямой угол — маленький квадрат
ctx.globalAlpha = 0.8;
ctx.beginPath();
@@ -1057,7 +1128,7 @@ class GeoSim {
// Подпись угла вдоль биссектрисы
if (bisLen > 1e-6) {
- const ldist = (Math.abs(angle - 90) < 2 ? SQ_SZ : ARC_R) + LBL_D;
+ const ldist = (explicitMark > 0 ? ARC_R + (explicitMark-1)*7 : Math.abs(angle - 90) < 2 ? SQ_SZ : ARC_R) + LBL_D;
const bx = bisX / bisLen, by = bisY / bisLen;
ctx.font = '10px Manrope,sans-serif';
ctx.fillStyle = col;
@@ -1071,21 +1142,26 @@ class GeoSim {
}
}
- // Прямые углы для foot-конструкций (основание высоты всегда 90°)
+ // Прямые углы для foot и altitude_foot конструкций
for (const obj of this.eng.points()) {
- if (!obj.derived || obj.constr !== 'foot') continue;
+ if (!obj.derived || (obj.constr !== 'foot' && obj.constr !== 'altitude_foot')) continue;
const F = this.vp.toCanvas(obj.x, obj.y);
- const P = this.eng.get(obj.srcPt);
- const sl = this.eng.get(obj.srcLine);
- if (!P || !sl) continue;
- let L1m, L2m;
- if (sl.type === 'derived_line') {
- L1m = { x: sl.ptX, y: sl.ptY };
- L2m = { x: sl.ptX + sl.dirX, y: sl.ptY + sl.dirY };
+ let P, L1m, L2m;
+ if (obj.constr === 'altitude_foot') {
+ P = this.eng.get(obj.ptA);
+ L1m = this._mpt(obj.ptB); L2m = this._mpt(obj.ptC);
} else {
- L1m = this._mpt(sl.p1Id); L2m = this._mpt(sl.p2Id);
+ P = this.eng.get(obj.srcPt);
+ const sl = this.eng.get(obj.srcLine);
+ if (!sl) continue;
+ if (sl.type === 'derived_line') {
+ L1m = { x: sl.ptX, y: sl.ptY };
+ L2m = { x: sl.ptX + sl.dirX, y: sl.ptY + sl.dirY };
+ } else {
+ L1m = this._mpt(sl.p1Id); L2m = this._mpt(sl.p2Id);
+ }
}
- if (!L1m || !L2m) continue;
+ if (!P || !L1m || !L2m) continue;
const L1 = this.vp.toCanvas(L1m.x, L1m.y);
const L2 = this.vp.toCanvas(L2m.x, L2m.y);
const Ppx = this.vp.toCanvas(P.x, P.y);
@@ -1838,6 +1914,188 @@ class GeoSim {
}
break;
}
+
+ /* ══ Phase 8: tick marks, arc marks ══ */
+
+ case 'tick': {
+ // Клик на отрезок или сторону полигона → циклически меняет метку (0→1→2→3→0)
+ const line = this._hitTestLine(px, py);
+ if (line) {
+ this._pushUndo();
+ if (line.virtual && line.polyId) {
+ const poly = this.eng.get(line.polyId);
+ if (poly) {
+ if (!poly.sideMarks) poly.sideMarks = new Array(poly.pointIds.length).fill(0);
+ const si = poly.pointIds.indexOf(line.p1Id);
+ if (si >= 0) poly.sideMarks[si] = ((poly.sideMarks[si] || 0) + 1) % 4;
+ }
+ } else {
+ const seg = this.eng.get(line.id);
+ if (seg) seg.tickMark = ((seg.tickMark || 0) + 1) % 4;
+ }
+ if (this.onUpdate) this.onUpdate(this.getStats());
+ }
+ break;
+ }
+
+ case 'arcmark': {
+ // Клик на вершину полигона → циклически меняет метку дуги (0→1→2→3→0)
+ const SNAP_PX = 14;
+ let foundPoly = null, foundIdx = -1;
+ outer8:
+ for (const poly of this.eng.byType('polygon')) {
+ for (let i = 0; i < poly.pointIds.length; i++) {
+ const p = this._p(poly.pointIds[i]);
+ if (p && Math.hypot(p.x - px, p.y - py) < SNAP_PX) {
+ foundPoly = poly; foundIdx = i; break outer8;
+ }
+ }
+ }
+ if (foundPoly && foundIdx >= 0) {
+ this._pushUndo();
+ if (!foundPoly.angleMarks) foundPoly.angleMarks = new Array(foundPoly.pointIds.length).fill(0);
+ foundPoly.angleMarks[foundIdx] = (foundPoly.angleMarks[foundIdx] + 1) % 4;
+ if (this.onUpdate) this.onUpdate(this.getStats());
+ }
+ break;
+ }
+
+ /* ══ Phase 7: altitude, median, centroid, orthocenter ══ */
+
+ case 'altitude': {
+ // Шаг 1: выбрать прямую (сторону), Шаг 2: выбрать вершину
+ if (!this._pendingLineRef) {
+ const hit = this._hitTestLine(px, py);
+ if (hit) {
+ this._pendingLineRef = hit;
+ if (this.onHintChange) this.onHintChange('altitude', 2);
+ }
+ } else {
+ this._pushUndo();
+ const vertex = this._ensurePoint(snapped);
+ const sl = this._pendingLineRef;
+ let L1, L2;
+ if (sl.type === 'derived_line') {
+ L1 = { x: sl.ptX, y: sl.ptY }; L2 = { x: sl.ptX+sl.dirX, y: sl.ptY+sl.dirY };
+ } else {
+ L1 = this._mpt(sl.p1Id); L2 = this._mpt(sl.p2Id);
+ }
+ if (L1 && L2) {
+ const f = gFoot({ x: vertex.x, y: vertex.y }, L1, L2);
+ const nFoot = this.eng.byType('point').filter(p=>p.constr==='foot').length;
+ const foot = this.eng.add({
+ type: 'point', derived: true, constr: 'foot',
+ srcLine: sl.id, srcPt: vertex.id,
+ x: f.x, y: f.y,
+ label: 'H' + (nFoot ? String.fromCharCode(0x2081 + nFoot) : '\u2081'),
+ style: { color: '#4ADE80', size: 4 }
+ });
+ // Отрезок-высота: вершина → основание
+ this.eng.add({ type: 'segment', p1Id: vertex.id, p2Id: foot.id,
+ style: { color: '#4ADE80', width: 1.5 } });
+ }
+ this._pendingLineRef = null; this._pending = []; this._preview = null;
+ if (this.onUpdate) this.onUpdate(this.getStats());
+ }
+ break;
+ }
+
+ case 'median': {
+ // 3 клика: вершина A, затем B и C (концы стороны) → середина M + отрезок AM
+ this._pending.push(snapped);
+ if (this._pending.length === 1) {
+ if (this.onHintChange) this.onHintChange('median', 2);
+ } else if (this._pending.length === 2) {
+ if (this.onHintChange) this.onHintChange('median', 3);
+ } else if (this._pending.length === 3) {
+ this._pushUndo();
+ const ptA = this._ensurePoint(this._pending[0]);
+ const ptB = this._ensurePoint(this._pending[1]);
+ const ptC = this._ensurePoint(this._pending[2]);
+ const nMid = this.eng.byType('point').filter(p=>p.constr==='midpoint').length;
+ const mid = this.eng.add({
+ type: 'point', derived: true, constr: 'midpoint',
+ srcA: ptB.id, srcB: ptC.id,
+ x: (ptB.x+ptC.x)/2, y: (ptB.y+ptC.y)/2,
+ label: 'M' + (nMid+1), style: { color: '#22d55e', size: 4 }
+ });
+ this.eng.add({ type: 'segment', p1Id: ptA.id, p2Id: mid.id,
+ style: { color: '#22d55e', width: 1.5 } });
+ this._pending = []; this._preview = null;
+ if (this.onUpdate) this.onUpdate(this.getStats());
+ }
+ break;
+ }
+
+ case 'centroid': {
+ // 3 клика: A, B, C → 3 медианы + точка центроид G
+ this._pending.push(snapped);
+ if (this._pending.length === 1) {
+ if (this.onHintChange) this.onHintChange('centroid', 2);
+ } else if (this._pending.length === 2) {
+ if (this.onHintChange) this.onHintChange('centroid', 3);
+ } else if (this._pending.length === 3) {
+ this._pushUndo();
+ const pA = this._ensurePoint(this._pending[0]);
+ const pB = this._ensurePoint(this._pending[1]);
+ const pC = this._ensurePoint(this._pending[2]);
+ const nG = this.eng.byType('point').filter(p=>p.constr==='centroid').length;
+ const col = '#A78BFA';
+ // 3 середины сторон
+ const mBC = this.eng.add({ type:'point', derived:true, constr:'midpoint', srcA:pB.id, srcB:pC.id, x:(pB.x+pC.x)/2, y:(pB.y+pC.y)/2, label:'M₁', style:{color:col,size:3} });
+ const mAC = this.eng.add({ type:'point', derived:true, constr:'midpoint', srcA:pA.id, srcB:pC.id, x:(pA.x+pC.x)/2, y:(pA.y+pC.y)/2, label:'M₂', style:{color:col,size:3} });
+ const mAB = this.eng.add({ type:'point', derived:true, constr:'midpoint', srcA:pA.id, srcB:pB.id, x:(pA.x+pB.x)/2, y:(pA.y+pB.y)/2, label:'M₃', style:{color:col,size:3} });
+ // 3 медианы
+ this.eng.add({ type:'segment', p1Id:pA.id, p2Id:mBC.id, style:{color:col, width:1.5} });
+ this.eng.add({ type:'segment', p1Id:pB.id, p2Id:mAC.id, style:{color:col, width:1.5} });
+ this.eng.add({ type:'segment', p1Id:pC.id, p2Id:mAB.id, style:{color:col, width:1.5} });
+ // Центроид
+ this.eng.add({ type:'point', derived:true, constr:'centroid',
+ ptA:pA.id, ptB:pB.id, ptC:pC.id,
+ x:(pA.x+pB.x+pC.x)/3, y:(pA.y+pB.y+pC.y)/3,
+ label: nG ? 'G'+(nG+1) : 'G', style:{color:col, size:6} });
+ this._pending = []; this._preview = null;
+ if (this.onUpdate) this.onUpdate(this.getStats());
+ }
+ break;
+ }
+
+ case 'orthocenter': {
+ // 3 клика: A, B, C → 3 высоты + точка ортоцентра H
+ this._pending.push(snapped);
+ if (this._pending.length === 1) {
+ if (this.onHintChange) this.onHintChange('orthocenter', 2);
+ } else if (this._pending.length === 2) {
+ if (this.onHintChange) this.onHintChange('orthocenter', 3);
+ } else if (this._pending.length === 3) {
+ this._pushUndo();
+ const pA = this._ensurePoint(this._pending[0]);
+ const pB = this._ensurePoint(this._pending[1]);
+ const pC = this._ensurePoint(this._pending[2]);
+ const nH = this.eng.byType('point').filter(p=>p.constr==='orthocenter').length;
+ const col = '#F97316';
+ const A = {x:pA.x,y:pA.y}, B = {x:pB.x,y:pB.y}, C = {x:pC.x,y:pC.y};
+ // Основания высот
+ const Ha = this.eng.add({ type:'point', derived:true, constr:'altitude_foot', ptA:pA.id, ptB:pB.id, ptC:pC.id, ...gFoot(A,B,C), label:'H_a', style:{color:col,size:3} });
+ const Hb = this.eng.add({ type:'point', derived:true, constr:'altitude_foot', ptA:pB.id, ptB:pA.id, ptC:pC.id, ...gFoot(B,A,C), label:'H_b', style:{color:col,size:3} });
+ const Hc = this.eng.add({ type:'point', derived:true, constr:'altitude_foot', ptA:pC.id, ptB:pA.id, ptC:pB.id, ...gFoot(C,A,B), label:'H_c', style:{color:col,size:3} });
+ // Отрезки-высоты
+ this.eng.add({ type:'segment', p1Id:pA.id, p2Id:Ha.id, style:{color:col, width:1.5} });
+ this.eng.add({ type:'segment', p1Id:pB.id, p2Id:Hb.id, style:{color:col, width:1.5} });
+ this.eng.add({ type:'segment', p1Id:pC.id, p2Id:Hc.id, style:{color:col, width:1.5} });
+ // Ортоцентр
+ const orth = gOrthocenter(A, B, C);
+ if (orth) {
+ this.eng.add({ type:'point', derived:true, constr:'orthocenter',
+ ptA:pA.id, ptB:pB.id, ptC:pC.id,
+ x:orth.x, y:orth.y, valid:true,
+ label: nH ? 'H'+(nH+1) : 'H', style:{color:col, size:6} });
+ }
+ this._pending = []; this._preview = null;
+ if (this.onUpdate) this.onUpdate(this.getStats());
+ }
+ break;
+ }
}
this.render();
}
diff --git a/frontend/lab.html b/frontend/lab.html
index 2d39cc4..13b2412 100644
--- a/frontend/lab.html
+++ b/frontend/lab.html
@@ -3896,6 +3896,26 @@
+ Элементы треугольника
+
+
Правильный многоугольник
+
+ Метки
+
+
Параметры