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import vtkCell from 'vtk.js/Sources/Common/DataModel/Cell';
import * as vtkMath from 'vtk.js/Sources/Common/Core/Math';
import vtkLine from 'vtk.js/Sources/Common/DataModel/Line';
import vtkPlane from 'vtk.js/Sources/Common/DataModel/Plane';
// ----------------------------------------------------------------------------
// Global methods
// ----------------------------------------------------------------------------
function computeNormalDirection(v1, v2, v3, n) {
// order is important!!! maintain consistency with triangle vertex order
const ax = v3[0] - v2[0];
const ay = v3[1] - v2[1];
const az = v3[2] - v2[2];
const bx = v1[0] - v2[0];
const by = v1[1] - v2[1];
const bz = v1[2] - v2[2];
n[0] = ay * bz - az * by;
n[1] = az * bx - ax * bz;
n[2] = ax * by - ay * bx;
}
function computeNormal(v1, v2, v3, n) {
computeNormalDirection(v1, v2, v3, n);
const length = Math.sqrt(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
if (length !== 0.0) {
n[0] /= length;
n[1] /= length;
n[2] /= length;
}
}
function intersectWithTriangle(p1, q1, r1, p2, q2, r2, tolerance = 1e-6) {
let coplanar = false;
const pt1 = [];
const pt2 = [];
const surfaceId = [];
const n1 = [];
const n2 = [];
// Compute supporting plane normals.
computeNormal(p1, q1, r1, n1);
computeNormal(p2, q2, r2, n2);
const s1 = -vtkMath.dot(n1, p1);
const s2 = -vtkMath.dot(n2, p2);
// Compute signed distances of points p1, q1, r1 from supporting
// plane of second triangle.
const dist1 = [
vtkMath.dot(n2, p1) + s2,
vtkMath.dot(n2, q1) + s2,
vtkMath.dot(n2, r1) + s2,
];
// If signs of all points are the same, all the points lie on the
// same side of the supporting plane, and we can exit early.
if (dist1[0] * dist1[1] > tolerance && dist1[0] * dist1[2] > tolerance) {
// vtkDebugMacro(<<"Same side supporting plane 1!");
return { intersect: false, coplanar, pt1, pt2, surfaceId };
}
// Do the same for p2, q2, r2 and supporting plane of first
// triangle.
const dist2 = [
vtkMath.dot(n1, p2) + s1,
vtkMath.dot(n1, q2) + s1,
vtkMath.dot(n1, r2) + s1,
];
// If signs of all points are the same, all the points lie on the
// same side of the supporting plane, and we can exit early.
if (dist2[0] * dist2[1] > tolerance && dist2[0] * dist2[2] > tolerance) {
// vtkDebugMacro(<<"Same side supporting plane 2!");
return { intersect: false, coplanar, pt1, pt2, surfaceId };
}
// Check for coplanarity of the supporting planes.
if (
Math.abs(n1[0] - n2[0]) < 1e-9 &&
Math.abs(n1[1] - n2[1]) < 1e-9 &&
Math.abs(n1[2] - n2[2]) < 1e-9 &&
Math.abs(s1 - s2) < 1e-9
) {
coplanar = true;
// vtkDebugMacro(<<"Coplanar!");
return { intersect: false, coplanar, pt1, pt2, surfaceId };
}
// There are more efficient ways to find the intersection line (if
// it exists), but this is clear enough.
const pts1 = [p1, q1, r1];
const pts2 = [p2, q2, r2];
// Find line of intersection (L = p + t*v) between two planes.
const n1n2 = vtkMath.dot(n1, n2);
const a = (s1 - s2 * n1n2) / (n1n2 * n1n2 - 1.0);
const b = (s2 - s1 * n1n2) / (n1n2 * n1n2 - 1.0);
const p = [
a * n1[0] + b * n2[0],
a * n1[1] + b * n2[1],
a * n1[2] + b * n2[2],
];
const v = vtkMath.cross(n1, n2, []);
vtkMath.normalize(v);
let index1 = 0;
let index2 = 0;
const t1 = [];
const t2 = [];
let ts1 = 50;
let ts2 = 50;
for (let i = 0; i < 3; i++) {
const id1 = i;
const id2 = (i + 1) % 3;
// Find t coordinate on line of intersection between two planes.
const val1 = vtkPlane.intersectWithLine(pts1[id1], pts1[id2], p2, n2);
if (val1.intersection && val1.t > 0 - tolerance && val1.t < 1 + tolerance) {
if (val1.t < 1 + tolerance && val1.t > 1 - tolerance) {
ts1 = index1;
}
t1[index1++] = vtkMath.dot(val1.x, v) - vtkMath.dot(p, v);
}
const val2 = vtkPlane.intersectWithLine(pts2[id1], pts2[id2], p1, n1);
if (val2.intersection && val2.t > 0 - tolerance && val2.t < 1 + tolerance) {
if (val2.t < 1 + tolerance && val2.t > 1 - tolerance) {
ts2 = index2;
}
t2[index2++] = vtkMath.dot(val2.x, v) - vtkMath.dot(p, v);
}
}
// If the value of the index is greater than 2, the intersecting point
// actually is intersected by all three edges. In this case, set the two
// edges to the two edges where the intersecting point is not the end point
Iif (index1 > 2) {
index1--;
// swap
const t12 = t1[2];
t1[2] = t1[ts1];
t1[ts1] = t12;
}
Iif (index2 > 2) {
index2--;
const t22 = t2[2];
t2[2] = t2[ts2];
t2[ts2] = t22;
}
// Check if only one edge or all edges intersect the supporting
// planes intersection.
Iif (index1 !== 2 || index2 !== 2) {
// vtkDebugMacro(<<"Only one edge intersecting!");
return { intersect: false, coplanar, pt1, pt2, surfaceId };
}
// Check for NaNs
Iif (
Number.isNaN(t1[0]) ||
Number.isNaN(t1[1]) ||
Number.isNaN(t2[0]) ||
Number.isNaN(t2[1])
) {
// vtkWarningMacro(<<"NaNs!");
return { intersect: false, coplanar, pt1, pt2, surfaceId };
}
if (t1[0] > t1[1]) {
// swap
const t11 = t1[1];
t1[1] = t1[0];
t1[0] = t11;
}
if (t2[0] > t2[1]) {
// swap
const t21 = t2[1];
t2[1] = t2[0];
t2[0] = t21;
}
// Handle the different interval configuration cases.
let tt1;
let tt2;
if (t1[1] < t2[0] || t2[1] < t1[0]) {
// vtkDebugMacro(<<"No Overlap!");
return { intersect: false, coplanar, pt1, pt2, surfaceId }; // No overlap
}
if (t1[0] < t2[0]) {
if (t1[1] < t2[1]) {
// First point on surface 2, second point on surface 1
surfaceId[0] = 2;
surfaceId[1] = 1;
tt1 = t2[0];
tt2 = t1[1];
} else {
// Both points belong to lines on surface 2
surfaceId[0] = 2;
surfaceId[1] = 2;
tt1 = t2[0];
tt2 = t2[1];
}
} // t1[0] >= t2[0]
else if (t1[1] < t2[1]) {
// Both points belong to lines on surface 1
surfaceId[0] = 1;
surfaceId[1] = 1;
tt1 = t1[0];
tt2 = t1[1];
} else {
// First point on surface 1, second point on surface 2
surfaceId[0] = 1;
surfaceId[1] = 2;
tt1 = t1[0];
tt2 = t2[1];
}
// Create actual intersection points.
vtkMath.multiplyAccumulate(p, v, tt1, pt1);
vtkMath.multiplyAccumulate(p, v, tt2, pt2);
return { intersect: true, coplanar, pt1, pt2, surfaceId };
}
// ----------------------------------------------------------------------------
// Static API
// ----------------------------------------------------------------------------
export const STATIC = {
computeNormalDirection,
computeNormal,
intersectWithTriangle,
};
// ----------------------------------------------------------------------------
// vtkTriangle methods
// ----------------------------------------------------------------------------
function vtkTriangle(publicAPI, model) {
// Set our className
model.classHierarchy.push('vtkTriangle');
publicAPI.getCellDimension = () => 2;
publicAPI.intersectWithLine = (p1, p2, tol, x, pcoords) => {
const outObj = {
subId: 0,
t: Number.MAX_VALUE,
intersect: 0,
betweenPoints: false,
};
pcoords[2] = 0.0;
const closestPoint = [];
const tol2 = tol * tol;
// Get normal for triangle
const pt1 = [];
const pt2 = [];
const pt3 = [];
model.points.getPoint(0, pt1);
model.points.getPoint(1, pt2);
model.points.getPoint(2, pt3);
const n = [];
const weights = [];
computeNormal(pt1, pt2, pt3, n);
if (n[0] !== 0 || n[1] !== 0 || n[2] !== 0) {
// Intersect plane of triangle with line
const plane = vtkPlane.intersectWithLine(p1, p2, pt1, n);
outObj.betweenPoints = plane.betweenPoints;
outObj.t = plane.t;
x[0] = plane.x[0];
x[1] = plane.x[1];
x[2] = plane.x[2];
if (!plane.intersection) {
pcoords[0] = 0.0;
pcoords[1] = 0.0;
outObj.intersect = 0;
return outObj;
}
// Evaluate position
const inside = publicAPI.evaluatePosition(
x,
closestPoint,
pcoords,
weights
);
if (inside.evaluation >= 0) {
if (inside.dist2 <= tol2) {
outObj.intersect = 1;
return outObj;
}
outObj.intersect = inside.evaluation;
return outObj;
}
}
// Normals are null, so the triangle is degenerated and
// we still need to check intersection between line and
// the longest edge.
const dist2Pt1Pt2 = vtkMath.distance2BetweenPoints(pt1, pt2);
const dist2Pt2Pt3 = vtkMath.distance2BetweenPoints(pt2, pt3);
const dist2Pt3Pt1 = vtkMath.distance2BetweenPoints(pt3, pt1);
if (!model.line) {
model.line = vtkLine.newInstance();
}
if (dist2Pt1Pt2 > dist2Pt2Pt3 && dist2Pt1Pt2 > dist2Pt3Pt1) {
model.line.getPoints().setPoint(0, pt1);
model.line.getPoints().setPoint(1, pt2);
} else if (dist2Pt2Pt3 > dist2Pt3Pt1 && dist2Pt2Pt3 > dist2Pt1Pt2) {
model.line.getPoints().setPoint(0, pt2);
model.line.getPoints().setPoint(1, pt3);
} else {
model.line.getPoints().setPoint(0, pt3);
model.line.getPoints().setPoint(1, pt1);
}
const intersectLine = model.line.intersectWithLine(p1, p2, tol, x, pcoords);
outObj.betweenPoints = intersectLine.betweenPoints;
outObj.t = intersectLine.t;
if (intersectLine.intersect) {
const pt3Pt1 = [];
const pt3Pt2 = [];
const pt3X = [];
// Compute r and s manually, using dot and norm.
for (let i = 0; i < 3; i++) {
pt3Pt1[i] = pt1[i] - pt3[i];
pt3Pt2[i] = pt2[i] - pt3[i];
pt3X[i] = x[i] - pt3[i];
}
pcoords[0] = vtkMath.dot(pt3X, pt3Pt1) / dist2Pt3Pt1;
pcoords[1] = vtkMath.dot(pt3X, pt3Pt2) / dist2Pt2Pt3;
outObj.intersect = 1;
return outObj;
}
pcoords[0] = 0.0;
pcoords[1] = 0.0;
outObj.intersect = 0;
return outObj;
};
publicAPI.evaluatePosition = (x, closestPoint, pcoords, weights) => {
// will return obj
const outObj = { subId: 0, dist2: 0, evaluation: -1 };
let i;
let j;
const pt1 = [];
const pt2 = [];
const pt3 = [];
const n = [];
let fabsn;
const rhs = [];
const c1 = [];
const c2 = [];
let det = 0;
let idx = 0;
const indices = [];
let dist2Point;
let dist2Line1;
let dist2Line2;
let closest = [];
const closestPoint1 = [];
const closestPoint2 = [];
const cp = [];
outObj.subId = 0;
pcoords[2] = 0.0;
// Get normal for triangle, only the normal direction is needed, i.e. the
// normal need not be normalized (unit length)
//
model.points.getPoint(1, pt1);
model.points.getPoint(2, pt2);
model.points.getPoint(0, pt3);
computeNormalDirection(pt1, pt2, pt3, n);
// Project point to plane
vtkPlane.generalizedProjectPoint(x, pt1, n, cp);
// Construct matrices. Since we have over determined system, need to find
// which 2 out of 3 equations to use to develop equations. (Any 2 should
// work since we've projected point to plane.)
let maxComponent = 0.0;
for (i = 0; i < 3; i++) {
// trying to avoid an expensive call to fabs()
Iif (n[i] < 0) {
fabsn = -n[i];
} else {
fabsn = n[i];
}
if (fabsn > maxComponent) {
maxComponent = fabsn;
idx = i;
}
}
for (j = 0, i = 0; i < 3; i++) {
if (i !== idx) {
indices[j++] = i;
}
}
for (i = 0; i < 2; i++) {
rhs[i] = cp[indices[i]] - pt3[indices[i]];
c1[i] = pt1[indices[i]] - pt3[indices[i]];
c2[i] = pt2[indices[i]] - pt3[indices[i]];
}
det = vtkMath.determinant2x2(c1, c2);
Iif (det === 0.0) {
pcoords[0] = 0.0;
pcoords[1] = 0.0;
outObj.evaluation = -1;
return outObj;
}
pcoords[0] = vtkMath.determinant2x2(rhs, c2) / det;
pcoords[1] = vtkMath.determinant2x2(c1, rhs) / det;
// Okay, now find closest point to element
weights[0] = 1 - (pcoords[0] + pcoords[1]);
weights[1] = pcoords[0];
weights[2] = pcoords[1];
if (
weights[0] >= 0.0 &&
weights[0] <= 1.0 &&
weights[1] >= 0.0 &&
weights[1] <= 1.0 &&
weights[2] >= 0.0 &&
weights[2] <= 1.0
) {
// projection distance
if (closestPoint) {
outObj.dist2 = vtkMath.distance2BetweenPoints(cp, x);
closestPoint[0] = cp[0];
closestPoint[1] = cp[1];
closestPoint[2] = cp[2];
}
outObj.evaluation = 1;
} else {
let t;
if (closestPoint) {
Iif (weights[1] < 0.0 && weights[2] < 0.0) {
dist2Point = vtkMath.distance2BetweenPoints(x, pt3);
dist2Line1 = vtkLine.distanceToLine(x, pt1, pt3, t, closestPoint1);
dist2Line2 = vtkLine.distanceToLine(x, pt3, pt2, t, closestPoint2);
if (dist2Point < dist2Line1) {
outObj.dist2 = dist2Point;
closest = pt3;
} else {
outObj.dist2 = dist2Line1;
closest = closestPoint1;
}
if (dist2Line2 < outObj.dist2) {
outObj.dist2 = dist2Line2;
closest = closestPoint2;
}
for (i = 0; i < 3; i++) {
closestPoint[i] = closest[i];
}
} else Iif (weights[2] < 0.0 && weights[0] < 0.0) {
dist2Point = vtkMath.distance2BetweenPoints(x, pt1);
dist2Line1 = vtkLine.distanceToLine(x, pt1, pt3, t, closestPoint1);
dist2Line2 = vtkLine.distanceToLine(x, pt1, pt2, t, closestPoint2);
if (dist2Point < dist2Line1) {
outObj.dist2 = dist2Point;
closest = pt1;
} else {
outObj.dist2 = dist2Line1;
closest = closestPoint1;
}
if (dist2Line2 < outObj.dist2) {
outObj.dist2 = dist2Line2;
closest = closestPoint2;
}
for (i = 0; i < 3; i++) {
closestPoint[i] = closest[i];
}
} else Iif (weights[1] < 0.0 && weights[0] < 0.0) {
dist2Point = vtkMath.distance2BetweenPoints(x, pt2);
dist2Line1 = vtkLine.distanceToLine(x, pt2, pt3, t, closestPoint1);
dist2Line2 = vtkLine.distanceToLine(x, pt1, pt2, t, closestPoint2);
if (dist2Point < dist2Line1) {
outObj.dist2 = dist2Point;
closest = pt2;
} else {
outObj.dist2 = dist2Line1;
closest = closestPoint1;
}
if (dist2Line2 < outObj.dist2) {
outObj.dist2 = dist2Line2;
closest = closestPoint2;
}
for (i = 0; i < 3; i++) {
closestPoint[i] = closest[i];
}
} else if (weights[0] < 0.0) {
const lineDistance = vtkLine.distanceToLine(
x,
pt1,
pt2,
closestPoint
);
outObj.dist2 = lineDistance.distance;
} else if (weights[1] < 0.0) {
const lineDistance = vtkLine.distanceToLine(
x,
pt2,
pt3,
closestPoint
);
outObj.dist2 = lineDistance.distance;
} else if (weights[2] < 0.0) {
const lineDistance = vtkLine.distanceToLine(
x,
pt1,
pt3,
closestPoint
);
outObj.dist2 = lineDistance.distance;
}
}
outObj.evaluation = 0;
}
return outObj;
};
publicAPI.evaluateLocation = (pcoords, x, weights) => {
const p0 = [];
const p1 = [];
const p2 = [];
model.points.getPoint(0, p0);
model.points.getPoint(1, p1);
model.points.getPoint(2, p2);
const u3 = 1.0 - pcoords[0] - pcoords[1];
for (let i = 0; i < 3; i++) {
x[i] = p0[i] * u3 + p1[i] * pcoords[0] + p2[i] * pcoords[1];
}
weights[0] = u3;
weights[1] = pcoords[0];
weights[2] = pcoords[1];
};
publicAPI.getParametricDistance = (pcoords) => {
let pDist;
let pDistMax = 0.0;
const pc = [];
pc[0] = pcoords[0];
pc[1] = pcoords[1];
pc[2] = 1.0 - pcoords[0] - pcoords[1];
for (let i = 0; i < 3; i++) {
Iif (pc[i] < 0.0) {
pDist = -pc[i];
} else Iif (pc[i] > 1.0) {
pDist = pc[i] - 1.0;
} else {
// inside the cell in the parametric direction
pDist = 0.0;
}
Iif (pDist > pDistMax) {
pDistMax = pDist;
}
}
return pDistMax;
};
}
// ----------------------------------------------------------------------------
// Object factory
// ----------------------------------------------------------------------------
const DEFAULT_VALUES = {};
// ----------------------------------------------------------------------------
export function extend(publicAPI, model, initialValues = {}) {
Object.assign(model, DEFAULT_VALUES, initialValues);
vtkCell.extend(publicAPI, model, initialValues);
vtkTriangle(publicAPI, model);
}
// ----------------------------------------------------------------------------
export const newInstance = macro.newInstance(extend, 'vtkTriangle');
// ----------------------------------------------------------------------------
export default { newInstance, extend, ...STATIC };
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