private static VertexInfo[][] tubeFromCurve(Pt[] pts, double radius, int revSteps)
{
var normals = new Pt[pts.Length];
normals[0] = ((pts[1] - pts[0]) * pt(0, 1, 0)).Normalize() * radius;
for (int i = 1; i < pts.Length - 1; i++)
{
normals[i] = normals[i - 1].ProjectOntoPlane((pts[i + 1] - pts[i]) + (pts[i] - pts[i - 1])).Normalize() * radius;
}
normals[pts.Length - 1] = normals[pts.Length - 2].ProjectOntoPlane(pts[pts.Length - 1] - pts[pts.Length - 2]).Normalize() * radius;
var axes = pts.Select((p, i) =>
i == 0 ? new { Start = pts[0], End = pts[1] } :
i == pts.Length - 1 ? new { Start = pts[pts.Length - 2], End = pts[pts.Length - 1] } :
new { Start = p, End = p + (pts[i + 1] - p) + (p - pts[i - 1]) }).ToArray();
return(Enumerable.Range(0, pts.Length)
.Select(ix => new { Axis = axes[ix], Perp = pts[ix] + normals[ix], Point = pts[ix] })
.Select(inf => Enumerable.Range(0, revSteps)
.Select(i => 360 * i / revSteps)
.Select(angle => inf.Perp.Rotate(inf.Axis.Start, inf.Axis.End, angle))
.Select(p => new VertexInfo {
Point = p, Normal = p - inf.Point
}).Reverse().ToArray())
.ToArray());
}
public static Pt RotateX(this Pt p, double angle)
{
return(new Pt(p.X, p.Y * cos(angle) - p.Z * sin(angle), p.Y * sin(angle) + p.Z * cos(angle)));
}
public static IEnumerable <Pt[]> Move(this IEnumerable <Pt[]> faces, Pt by)
{
return(faces.Select(face => Move(face, by)));
}
public static Pt[][] Move(this Pt[][] faces, Pt by)
{
return(faces.Select(face => Move(face, by)).ToArray());
}
public static IEnumerable <Pt> Move(this IEnumerable <Pt> face, Pt by)
{
return(face.Select(p => p + by));
}
public static Pt[] Move(this Pt[] face, Pt by)
{
return(face.Select(p => p + by).ToArray());
}
public static Mesh GenerateWire(System.Random rnd, int lengthIndex, int color, WirePiece piece, bool highlight)
{
var length = GetWireLength(lengthIndex);
var thickness = highlight ? _wireRadiusHighlight : _wireRadius;
var firstControlHeight = highlight ? _firstControlHeightHighlight : _firstControlHeight;
var interpolateHeight = highlight ? _interpolateHeightHighlight : _interpolateHeight;
var start = pt(0, 0, 0);
var startControl = pt(length / 10, 0, firstControlHeight);
var endControl = pt(length * 9 / 10, 0, firstControlHeight);
var end = pt(length, 0, 0);
var numSegments = new[] { 6, 4, 4 }[lengthIndex];
var bézierSteps = 16;
var tubeRevSteps = 16;
var interpolateStart = pt(0, 0, interpolateHeight);
var interpolateEnd = pt(length, 0, interpolateHeight);
var intermediatePoints = newArray(numSegments - 1, i => interpolateStart + (interpolateEnd - interpolateStart) * (i + 1) / numSegments + pt(rnd.NextDouble() - .5, rnd.NextDouble() - .5, rnd.NextDouble() - .5) * _wireMaxSegmentDeviation);
var deviations = newArray(numSegments - 1, _ => pt(rnd.NextDouble(), rnd.NextDouble(), rnd.NextDouble()) * _wireMaxBézierDeviation);
if (piece == WirePiece.Uncut)
{
var points =
new[] { new { ControlBefore = default(Pt), Point = start, ControlAfter = startControl } }
.Concat(intermediatePoints.Select((p, i) => new { ControlBefore = p - deviations[i], Point = p, ControlAfter = p + deviations[i] }))
.Concat(new[] { new { ControlBefore = endControl, Point = end, ControlAfter = default(Pt) } })
.SelectConsecutivePairs(false, (one, two) => bézier(one.Point, one.ControlAfter, two.ControlBefore, two.Point, bézierSteps))
.SelectMany((x, i) => i == 0 ? x : x.Skip(1))
.ToArray();
return(toMesh(createFaces(false, true, tubeFromCurve(points, thickness, tubeRevSteps)), _colors[color]));
}
var partialWire = new Func <IEnumerable <CPC>, IEnumerable <VertexInfo[]> >(pts =>
{
var points = pts
.SelectConsecutivePairs(false, (one, two) => bézier(one.Point, one.ControlAfter, two.ControlBefore, two.Point, bézierSteps))
.SelectMany((x, i) => i == 0 ? x : x.Skip(1))
.ToArray();
var reserveForCopper = 6;
var discardCopper = 2;
if (piece == WirePiece.Cut)
{
var tube = tubeFromCurve(points, thickness, tubeRevSteps).SkipLast(reserveForCopper).ToArray();
var capCenter = points[points.Length - 1 - reserveForCopper];
var normal = capCenter - points[points.Length - 2 - reserveForCopper];
var cap = tube[tube.Length - 1].SelectConsecutivePairs(true, (v1, v2) => new[] { capCenter, v2.Point, v1.Point }.Select(p => new VertexInfo {
Point = p, Normal = normal
}).ToArray()).ToArray();
return(createFaces(false, true, tube).Concat(cap));
}
else
{
var copper = tubeFromCurve(points.TakeLast(reserveForCopper + 2).SkipLast(discardCopper).ToArray(), thickness / 2, tubeRevSteps).Skip(1).ToArray();
var copperCapCenter = points[points.Length - 1 - discardCopper];
var copperNormal = copperCapCenter - points[points.Length - 2];
var copperCap = copper[copper.Length - 1].SelectConsecutivePairs(true, (v1, v2) => new[] { copperCapCenter, v2.Point, v1.Point }.Select(p => new VertexInfo {
Point = p, Normal = copperNormal
}).ToArray()).ToArray();
return(createFaces(false, true, copper).Concat(copperCap));
}
});
var rotAngle = (rnd.NextDouble() * 7 + 5) * (rnd.Next(2) == 0 ? -1 : 1);
var rotAxisStart = new Pt(0, 0, 0);
var rotAxisEnd = new Pt(rnd.NextDouble() * .01, rnd.NextDouble() * .01, 1);
Func <Pt, Pt> rot = p => p.Rotate(rotAxisStart, rotAxisEnd, rotAngle);
var beforeCut =
new[] { new CPC {
ControlBefore = default(Pt), Point = start, ControlAfter = startControl
} }
.Concat(intermediatePoints.Take(numSegments / 2).Select((p, i) => new CPC {
ControlBefore = rot(p - deviations[i]), Point = rot(p), ControlAfter = rot(p + deviations[i])
}));
var bcTube = partialWire(beforeCut);
var cutOffPoint = (numSegments - 1) / 2;
rotAngle = (rnd.NextDouble() * 7 + 5) * (rnd.Next(2) == 0 ? -1 : 1);
rotAxisStart = new Pt(length, 0, 0);
rotAxisEnd = new Pt(length + rnd.NextDouble() * .01, rnd.NextDouble() * .01, 1);
var afterCut =
new[] { new CPC {
ControlBefore = default(Pt), Point = end, ControlAfter = endControl
} }
.Concat(intermediatePoints.Skip(cutOffPoint).Select((p, i) => new CPC {
ControlBefore = rot(p + deviations[i + cutOffPoint]), Point = rot(p), ControlAfter = rot(p - deviations[i + cutOffPoint])
}).Reverse());
var acTube = partialWire(afterCut);
return(toMesh(bcTube.Concat(acTube).ToArray(), _colors[color]));
}
private static IEnumerable <Pt> bézier(Pt start, Pt control1, Pt control2, Pt end, int steps)
{
return(Enumerable.Range(0, steps)
.Select(i => (double)i / (steps - 1))
.Select(t => pow(1 - t, 3) * start + 3 * pow(1 - t, 2) * t * control1 + 3 * (1 - t) * t * t * control2 + pow(t, 3) * end));
}