// Calculates a gear with perfect equilateral triangles as teeth teeth
// TODO: position it properly!
public static GearDescription DescribeGear(float toothSideLength, int teeth)
{
Assert(toothSideLength > float.Epsilon);
Assert(teeth > 0);
var halfToothSideLength = toothSideLength / 2.0f;
//var diameter = Diameter(toothSideLength, teeth);
var rootDiameter = GetRootDiameter(toothSideLength, teeth);
var toothHeight = (float)(halfToothSideLength * Math.Sqrt(3.0f));
var angleStep = MathHelper.TwoPi / teeth;
var description = new GearDescription(rootDiameter + (toothHeight * 2), rootDiameter, teeth);
var center = new Vector2(0, 0);
var lastPosition = new Vector2(rootDiameter / 2, -halfToothSideLength);
var lastAngle = 0.0f;
for (var i = 0; i < teeth; i++)
{
var min = lastPosition;
var forward = Vector2.TransformNormal(Vector2.UnitY, Matrix.CreateRotationZ(lastAngle));
var max = min + (forward * toothSideLength);
var tipBase = (min + max) / 2.0f;
var normal = Vector2.Normalize(tipBase - center);
var tipTop = tipBase + (normal * toothHeight);
description.ClockwiseEdges.Add(new LineDescription(tipTop, min));
description.CounterClockwiseEdges.Add(new LineDescription(tipTop, max));
description.Edges.Add(new LineDescription(min, max));
//description.ClockwiseEdges.Add(new LineDescription(tipTop, min));
//description.CounterClockwiseEdges.Add(new LineDescription(tipTop, max));
//description.ClockwiseEdges.Add(new LineDescription(center, tipBase));
//description.CounterClockwiseEdges.Add(new LineDescription(min, max));
lastPosition = max;
lastAngle += angleStep;
}
return(description);
//var rootDiameter = (toothSideLength * teeth) / MathHelper.Pi;
//// The height of an equilateral triangle is the length of a side divided by 2 time sqrt(3)
//var diameterDifference = (float)(toothSideLength * Math.Sqrt(3.0f));
//var outsideDiameter = rootDiameter + diameterDifference;
//return DescribeGear(outsideDiameter, rootDiameter, teeth, 0.0f);
}
public static GearDescription DescribeGear(float outsideDiameter, float rootDiameter, int teeth, float profileRatio)
{
Assert(outsideDiameter > rootDiameter);
Assert(teeth > 0);
Assert(profileRatio >= 0.0f && profileRatio < 1.0f);
var outsideRadius = outsideDiameter / 2.0f;
var rootRadius = rootDiameter / 2.0f;
var description = new GearDescription(outsideDiameter, rootDiameter, teeth);
var stepSize = MathHelper.TwoPi / teeth;
var tipStepSize = stepSize / 2.0f * profileRatio;
var riseStepSize = (stepSize - (tipStepSize * 2.0f)) / 2.0f;
var fallStepSize = riseStepSize;
// We're traversing the outline of the gear in a counter clockwise fashion
// starting at the three on the clock
for (var i = 0; i < teeth; i++)
{
var position = stepSize * i;
var riseStart = Vertex(position, rootRadius);
position += riseStepSize;
var riseEnd = Vertex(position, outsideRadius);
position += tipStepSize;
var fallStart = Vertex(position, outsideRadius);
position += fallStepSize;
var fallEnd = Vertex(position, rootRadius);
position = stepSize * (i + 1);
var next = Vertex(position, rootRadius);
var rise = new LineDescription(riseStart, riseEnd);
description.ClockwiseEdges.Add(rise);
description.Edges.Add(rise);
if (profileRatio > 0.0f)
{
var tip = new LineDescription(riseEnd, fallStart);
description.Edges.Add(tip);
}
var fall = new LineDescription(fallStart, fallEnd);
description.CounterClockwiseEdges.Add(fall);
description.Edges.Add(fall);
var connection = new LineDescription(fallEnd, next);
description.Edges.Add(connection);
}
return(description);
}
private List <Line> CreateGear(GraphicsDevice device, Vector3 position, float outsideDiameter, float rootDiameter, int teeth, float profileRatio)
{
var gear = new List <Line>();
var description = GearDescription.DescribeGear(outsideDiameter, rootDiameter, teeth, profileRatio);
for (var i = 0; i < description.ClockwiseEdges.Count; i++)
{
var edge = description.ClockwiseEdges[i];
var line = new Line(device, Color.Blue, edge.A, edge.B);
line.Position = position;
gear.Add(line);
}
for (var i = 0; i < description.CounterClockwiseEdges.Count; i++)
{
var edge = description.CounterClockwiseEdges[i];
var line = new Line(device, Color.Red, edge.A, edge.B);
line.Position = position;
gear.Add(line);
}
return(gear);
}