/// <summary>
/// Returns points in a defined spiral.
/// </summary>
/// <param name="origin">Center position of the spiral.</param>
/// <param name="direction">Direction in which the spiral spans.</param>
/// <param name="extent">Length of the spiral along the direction.</param>
/// <param name="innerRadius">Inner radius of the spiral; the distance between the center and the first point of the spiral.</param>
/// <param name="outerRadius">Outer radius of the spiral; the distance from the center to the last point of the spiral.</param>
/// <param name="turns">Number of times the spiral turns in itself.</param>
/// <param name="points">Number of points in the spiral.</param>
/// <param name="rotation">Rotation of the spiral along the direction.</param>
/// <returns></returns>
public static List <Vector3> Spiral(Vector3 origin, Vector3 direction, float extent, float innerRadius, float outerRadius, int turns, int points, float rotation)
{
if (points <= 1 || innerRadius < 0)
{
return(null);
}
Vector3 circleNormal = direction - origin;
Components.Plane plane = new Components.Plane(direction);
float width = (outerRadius - innerRadius) / (points - 1);
float height = extent / (points - 1);
float angleBetweenPoints = turns * 360 / (points - 1);
List <Vector3> spiral = new List <Vector3>();
for (int i = 0; i < points; i++)
{
float separationAngle = rotation + i * angleBetweenPoints;
Vector3 originDeviation = GetPoint(origin, origin + direction, height * i);
Vector3 point = plane.GetPoint(originDeviation, innerRadius + width * i, separationAngle);
spiral.Add(point);
}
return(spiral);
}
/// <summary>
/// Returns points in a defined arc.
/// </summary>
/// <param name="origin">Center from which the arc is drawn.</param>
/// <param name="normal">Normal vector of the arc; the direction in which it is pointing.</param>
/// <param name="amplitude">Angle, in degrees, covered by the arc. 360 is a full circle.</param>
/// <param name="horizontalRadius">Horizontal radius of an elliptic arc.</param>
/// <param name="verticalRadius">Vertical radius of an elliptic arc.</param>
/// <param name="radius">Radius of the arc; the distance between its center and a point.</param>
/// <param name="points">Number of points in the arc.</param>
/// <param name="rotation">Rotation of the circle; change the position of the first point.</param>
/// <returns></returns>
public static List <Vector3> Arc(Vector3 origin, Vector3 normal, float amplitude, float horizontalRadius, float verticalRadius, int points, float rotation)
{
if (horizontalRadius <= 0f || verticalRadius <= 0f)
{
return(null);
}
Vector3 arcNormal = normal - origin;
Components.Plane plane = new Components.Plane(arcNormal);
float amplitudeAngle = ClampAngle(amplitude);
float angleBetweenPoints = 0f;
if (amplitude < 360)
{
angleBetweenPoints = amplitude / (points - 1);
}
else
{
angleBetweenPoints = amplitude / points;
}
List <Vector3> circle = new List <Vector3>();
for (int i = 0; i < points; i++)
{
float separationAngle = rotation + i * angleBetweenPoints;
Vector3 point = plane.GetPoint(origin, horizontalRadius, verticalRadius, separationAngle);
circle.Add(point);
}
return(circle);
}
/// <summary>
/// Returns a path of zigzaguing points.
/// </summary>
/// <param name="origin">Origin of the path.</param>
/// <param name="direction">Direction in which the path extents.</param>
/// <param name="deviation">Deviation of the path center from the origin. Values on range [-1, 1]: first point, center, first turning point.</param>
/// <param name="extent">Length of the path.</param>
/// <param name="amplitude">Distance between the two sides of the zigzag.</param>
/// <param name="turns">Number of turning points of the path.</param>
/// <param name="subdivisions">Number of divisions of the vector represented by two turning points.</param>
/// <param name="rotation">Rotation of the path around the direction vector.</param>
/// <returns></returns>
public static List <Vector3> Zigzag(Vector3 origin, Vector3 direction, int deviation, float extent, float amplitude, int turns, int subdivisions, float rotation)
{
Components.Plane plane = new Components.Plane(direction);
float width = amplitude / 2;
float span = extent / (turns - 1);
float horizontalDeviation = width * Mathf.Clamp(deviation, -1, 1);
float vectorDirection = 1;
List <Vector3> vectors = new List <Vector3>();
for (int i = 0; i < turns; i++)
{
Vector3 point = new Vector3();
point.x = vectorDirection * width + horizontalDeviation;
point.y = 0f;
point.z = span * i;
point = plane.Rotate(point, rotation, Components.Plane.Axis.N);
point = origin + plane.TransformPoint(point);
vectors.Add(point);
vectorDirection = -vectorDirection;
}
if (subdivisions <= 1)
{
return(vectors);
}
List <Vector3> points = new List <Vector3>();
for (int i = 1; i < vectors.Count; i++)
{
List <Vector3> dividedVector = Subdivide(vectors[i - 1], vectors[i], subdivisions);
points.AddRange(dividedVector);
}
points = points.Distinct().ToList();
return(points);
}
/// <summary>
/// Returns points in a defined wave.
/// </summary>
/// <param name="origin">Origin of the wave.</param>
/// <param name="direction">Direction in which the wave spans.</param>
/// <param name="extent">Length of th wave.</param>
/// <param name="amplitude">Amplitude of the wave; the distance between opposing peaks.</param>
/// <param name="frequency">Frecuency of periods in the wave.</param>
/// <param name="points">Points to draw accross the wave.</param>
/// <param name="rotation">Rotation of the wave around the direction vector.</param>
/// <returns></returns>
public static List <Vector3> Wave(Vector3 origin, Vector3 direction, float extent, float amplitude, float frequency, int points, float rotation)
{
Components.Plane plane = new Components.Plane(direction);
float separation = extent / (points - 1);
List <Vector3> wavePoints = new List <Vector3>();
for (int i = 0; i < points; i++)
{
Vector3 point = new Vector3();
point.x = amplitude * Mathf.Sin(frequency * (separation * i));
point.y = 0f;
point.z = separation * i;
point = plane.Rotate(point, rotation, Components.Plane.Axis.N);
point = origin + plane.TransformPoint(point);
wavePoints.Add(point);
}
return(wavePoints);
}
/// <summary>
/// Returns a point at given degrees and distance from origin around the normal of a geometrical plane.
/// </summary>
/// <param name="origin"></param>
/// <param name="radius"></param>
/// <param name="degrees"></param>
/// <returns></returns>
public static Vector3 GetPoint(Vector3 origin, Vector3 normal, float radius, float degrees)
{
Components.Plane plane = new Components.Plane(normal);
return(plane.GetPoint(origin, radius, degrees));
}