public static MeshDraft FlatSphere(float radius, int longitudeSegments, int latitudeSegments)
{
float longitudeSegmentAngle = Mathf.PI * 2 / longitudeSegments;
float latitudeSegmentAngle = Mathf.PI / latitudeSegments;
float currentLatitude = -Mathf.PI / 2;
var rings = new List <List <Vector3> >(latitudeSegments);
for (var i = 0; i <= latitudeSegments; i++)
{
var currentLongitude = 0f;
var ring = new List <Vector3>(longitudeSegments);
for (int j = 0; j < longitudeSegments; j++)
{
ring.Add(PTUtils.PointOnSphere(radius, currentLongitude, currentLatitude));
currentLongitude -= longitudeSegmentAngle;
}
rings.Add(ring);
currentLatitude += latitudeSegmentAngle;
}
var draft = new MeshDraft {
name = "Flat sphere"
};
for (int i = 0; i < rings.Count - 1; i++)
{
draft.Add(FlatBand(rings[i], rings[i + 1]));
}
return(draft);
}
/// <summary>
/// Constructs a icosahedron draft
/// </summary>
public static MeshDraft Icosahedron(float radius, bool generateUV = true)
{
const float magicAngle = 26.56505f;
const float segmentAngle = 72;
float lowerAngle = 0;
float upperAngle = segmentAngle / 2;
var lowerRing = new Vector3[5];
var upperRing = new Vector3[5];
for (var i = 0; i < 5; i++)
{
lowerRing[i] = PTUtils.PointOnSphere(radius, lowerAngle, -magicAngle);
upperRing[i] = PTUtils.PointOnSphere(radius, upperAngle, magicAngle);
lowerAngle += segmentAngle;
upperAngle += segmentAngle;
}
var draft = new MeshDraft {
name = "Icosahedron"
}
.AddBaselessPyramid(new Vector3(0, radius, 0), upperRing, generateUV)
.AddFlatTriangleBand(lowerRing, upperRing, generateUV)
.AddBaselessPyramid(new Vector3(0, -radius, 0), lowerRing, generateUV, true);
return(draft);
}
public static MeshDraft Icosahedron(float radius)
{
float magicAngle = Mathf.PI * 26.56505f / 180;
float segmentAngle = Mathf.PI * 72 / 180;
float currentAngle = 0f;
var upperRing = new List <Vector3>(5);
for (var i = 0; i < 5; i++)
{
upperRing.Add(PTUtils.PointOnSphere(radius, currentAngle, magicAngle));
currentAngle -= segmentAngle;
}
currentAngle = segmentAngle / 2;
var lowerRing = new List <Vector3>(5);
for (var i = 0; i < 5; i++)
{
lowerRing.Add(PTUtils.PointOnSphere(radius, currentAngle, -magicAngle));
currentAngle -= segmentAngle;
}
var draft = BaselessPyramid(new Vector3(0, -radius, 0), lowerRing);
draft.Add(FlatBand(lowerRing, upperRing));
upperRing.Reverse();
draft.Add(BaselessPyramid(new Vector3(0, radius, 0), upperRing));
draft.name = "Icosahedron";
return(draft);
}
/// <summary>
/// Constructs a tetrahedron draft
/// </summary>
public static MeshDraft Tetrahedron(float radius, bool generateUV = true)
{
const float tetrahedralAngle = -19.471220333f;
var vertex0 = new Vector3(0, radius, 0);
var vertex1 = PTUtils.PointOnSphere(radius, 0, tetrahedralAngle);
var vertex2 = PTUtils.PointOnSphere(radius, 120, tetrahedralAngle);
var vertex3 = PTUtils.PointOnSphere(radius, 240, tetrahedralAngle);
var draft = new MeshDraft {
name = "Tetrahedron"
};
if (generateUV)
{
var uv0 = new Vector2(0, 0);
var uv1 = new Vector2(0.5f, 1);
var uv2 = new Vector2(1, 0);
draft.AddTriangle(vertex2, vertex0, vertex1, uv0, uv1, uv2)
.AddTriangle(vertex2, vertex1, vertex3, uv0, uv1, uv2)
.AddTriangle(vertex3, vertex0, vertex2, uv0, uv1, uv2)
.AddTriangle(vertex1, vertex0, vertex3, uv0, uv1, uv2);
}
else
{
draft.AddTriangle(vertex2, vertex0, vertex1)
.AddTriangle(vertex2, vertex1, vertex3)
.AddTriangle(vertex3, vertex0, vertex2)
.AddTriangle(vertex1, vertex0, vertex3);
}
return(draft);
}
/// <summary>
/// Constructs a dodecahedron draft
/// </summary>
public static MeshDraft Dodecahedron(float radius)
{
const float magicAngle1 = 52.62263590f;
const float magicAngle2 = 10.81231754f;
const float segmentAngle = 72;
float lowerAngle = 0;
float upperAngle = segmentAngle / 2;
var lowerCap = new Vector3[5];
var lowerRing = new Vector3[5];
var upperCap = new Vector3[5];
var upperRing = new Vector3[5];
for (var i = 0; i < 5; i++)
{
lowerCap[i] = PTUtils.PointOnSphere(radius, lowerAngle, -magicAngle1);
lowerRing[i] = PTUtils.PointOnSphere(radius, lowerAngle, -magicAngle2);
upperCap[i] = PTUtils.PointOnSphere(radius, upperAngle, magicAngle1);
upperRing[i] = PTUtils.PointOnSphere(radius, upperAngle, magicAngle2);
lowerAngle += segmentAngle;
upperAngle += segmentAngle;
}
var draft = new MeshDraft {
name = "Dodecahedron"
}
.AddTriangleFan(upperCap, Vector3.up)
.AddFlatTriangleBand(upperRing, upperCap, false)
.AddFlatTriangleBand(lowerRing, upperRing, false)
.AddFlatTriangleBand(lowerCap, lowerRing, false)
.AddTriangleFan(lowerCap, Vector3.down, true);
return(draft);
}
public static MeshDraft Sphere(float radius, int longitudeSegments, int latitudeSegments)
{
var draft = new MeshDraft {
name = "Sphere"
};
float longitudeSegmentAngle = Mathf.PI * 2 / longitudeSegments;
float latitudeSegmentAngle = Mathf.PI / latitudeSegments;
float currentLatitude = -Mathf.PI / 2;
for (var ring = 0; ring <= latitudeSegments; ring++)
{
var currentLongitude = 0f;
for (int i = 0; i < longitudeSegments; i++)
{
var point = PTUtils.PointOnSphere(radius, currentLongitude, currentLatitude);
draft.vertices.Add(point);
draft.normals.Add(point.normalized);
draft.uv.Add(new Vector2((float)i / longitudeSegments, (float)ring / latitudeSegments));
currentLongitude -= longitudeSegmentAngle;
}
currentLatitude += latitudeSegmentAngle;
}
int i0, i1, i2, i3;
for (int ring = 0; ring < latitudeSegments; ring++)
{
for (int i = 0; i < longitudeSegments - 1; i++)
{
i0 = ring * longitudeSegments + i;
i1 = (ring + 1) * longitudeSegments + i;
i2 = ring * longitudeSegments + i + 1;
i3 = (ring + 1) * longitudeSegments + i + 1;
draft.triangles.AddRange(new[] { i0, i1, i2 });
draft.triangles.AddRange(new[] { i2, i1, i3 });
}
i0 = (ring + 1) * longitudeSegments - 1;
i1 = (ring + 2) * longitudeSegments - 1;
i2 = ring * longitudeSegments;
i3 = (ring + 1) * longitudeSegments;
draft.triangles.AddRange(new[] { i0, i1, i2 });
draft.triangles.AddRange(new[] { i2, i1, i3 });
}
return(draft);
}
public static MeshDraft Dodecahedron(float radius)
{
const float magicAngle1 = 52.62263590f;
const float magicAngle2 = 10.81231754f;
const float segmentAngle = 72;
float currentAngle = 0;
var lowerCap = new List <Vector3>();
var lowerRing = new List <Vector3>();
for (var i = 0; i < 5; i++)
{
lowerCap.Add(PTUtils.PointOnSphere(radius, currentAngle, -magicAngle1));
lowerRing.Add(PTUtils.PointOnSphere(radius, currentAngle, -magicAngle2));
currentAngle -= segmentAngle;
}
currentAngle = -segmentAngle / 2;
var upperCap = new List <Vector3>();
var upperRing = new List <Vector3>();
for (var i = 0; i < 5; i++)
{
upperCap.Add(PTUtils.PointOnSphere(radius, currentAngle, magicAngle1));
upperRing.Add(PTUtils.PointOnSphere(radius, currentAngle, magicAngle2));
currentAngle -= segmentAngle;
}
var draft = new MeshDraft {
name = "Dodecahedron"
}
.AddTriangleFan(lowerCap)
.Add(FlatBand(lowerCap, lowerRing))
.Add(FlatBand(lowerRing, upperRing))
.Add(FlatBand(upperRing, upperCap));
upperCap.Reverse();
draft.AddTriangleFan(upperCap);
return(draft);
}
public static MeshDraft Dodecahedron(float radius)
{
float magicAngle1 = Mathf.PI * 52.62263590f / 180;
float magicAngle2 = Mathf.PI * 10.81231754f / 180;
float segmentAngle = Mathf.PI * 2 / 5;
float currentAngle = 0f;
var lowerCap = new List <Vector3>();
var lowerRing = new List <Vector3>();
for (var i = 0; i <= 5; i++)
{
lowerCap.Add(PTUtils.PointOnSphere(radius, currentAngle, -magicAngle1));
lowerRing.Add(PTUtils.PointOnSphere(radius, currentAngle, -magicAngle2));
currentAngle -= segmentAngle;
}
currentAngle = -segmentAngle / 2;
var upperCap = new List <Vector3>();
var upperRing = new List <Vector3>();
for (var i = 0; i <= 5; i++)
{
upperCap.Add(PTUtils.PointOnSphere(radius, currentAngle, magicAngle1));
upperRing.Add(PTUtils.PointOnSphere(radius, currentAngle, magicAngle2));
currentAngle -= segmentAngle;
}
var draft = TriangleFan(lowerCap);
draft.Add(FlatBand(lowerCap, lowerRing));
draft.Add(FlatBand(lowerRing, upperRing));
draft.Add(FlatBand(upperRing, upperCap));
upperCap.Reverse();
draft.Add(TriangleFan(upperCap));
draft.name = "Dodecahedron";
return(draft);
}
public static MeshDraft Tetrahedron(float radius)
{
float tetrahedralAngle = Mathf.PI * -19.471220333f / 180;
float segmentAngle = Mathf.PI * 2 / 3;
float currentAngle = 0f;
var vertices = new List <Vector3>(4)
{
new Vector3(0, radius, 0)
};
for (var i = 1; i < 4; i++)
{
vertices.Add(PTUtils.PointOnSphere(radius, currentAngle, tetrahedralAngle));
currentAngle += segmentAngle;
}
var draft = Triangle(vertices[0], vertices[1], vertices[2]);
draft.Add(Triangle(vertices[1], vertices[3], vertices[2]));
draft.Add(Triangle(vertices[0], vertices[2], vertices[3]));
draft.Add(Triangle(vertices[0], vertices[3], vertices[1]));
draft.name = "Tetrahedron";
return(draft);
}
public static MeshDraft Tetrahedron(float radius)
{
const float tetrahedralAngle = -19.471220333f;
const float segmentAngle = 120;
float currentAngle = 0;
var vertices = new List <Vector3>(4)
{
new Vector3(0, radius, 0)
};
for (var i = 1; i < 4; i++)
{
vertices.Add(PTUtils.PointOnSphere(radius, currentAngle, tetrahedralAngle));
currentAngle += segmentAngle;
}
return(new MeshDraft {
name = "Tetrahedron"
}
.AddTriangle(vertices[0], vertices[1], vertices[2])
.AddTriangle(vertices[1], vertices[3], vertices[2])
.AddTriangle(vertices[0], vertices[2], vertices[3])
.AddTriangle(vertices[0], vertices[3], vertices[1]));
}
/// <summary>
/// Returns a point on the sphere at the given coordinates
/// </summary>
public Vector3 GetPoint(float horizontalAngle, float verticalAngle)
{
return(center + PTUtils.PointOnSphere(radius, horizontalAngle, verticalAngle));
}
