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Merge pull request #2 from EsProgram/translate-en
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英語翻訳
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@EsProgram
EsProgram authored Mar 1, 2017
2 parents 7b26213 + 220b534 commit 46c0c94
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207 changes: 90 additions & 117 deletions Assets/TexturePaint/Script/Core/DynamicCanvas.cs
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104 changes: 48 additions & 56 deletions Assets/TexturePaint/Script/Core/Math.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -7,19 +7,17 @@ namespace Es.TexturePaint
{
public static class Math
{
/// <summary>
/// 誤差許容範囲
/// </summary>
private const float TOLERANCE = 1E-2f;

/// <summary>
/// 点pが与えられた3点のなす三角形平面上に存在するかを調査する
/// Determine if there are points in the plane.
/// </summary>
/// <param name="p">調査点p</param>
/// <param name="t1">三角形をなす頂点</param>
/// <param name="t2">三角形をなす頂点</param>
/// <param name="t3">三角形をなす頂点</param>
/// <returns>点pが三角形平面上に存在するかどうか</returns>
/// <param name="p">Points to investigate.</param>
/// <param name="t1">Plane point.</param>
/// <param name="t2">Plane point.</param>
/// <param name="t3">Plane point.</param>
/// <summary>
/// <returns>Whether points exist in the triangle plane.</returns>
public static bool ExistPointInPlane(Vector3 p, Vector3 t1, Vector3 t2, Vector3 t3)
{
var v1 = t2 - t1;
Expand All @@ -34,25 +32,25 @@ public static bool ExistPointInPlane(Vector3 p, Vector3 t1, Vector3 t2, Vector3
}

/// <summary>
/// 点pが辺(v1,v2)上に存在するかどうかを調査する
/// Investigate whether a point exists on an edge.
/// </summary>
/// <param name="p">調査点</param>
/// <param name="v1">辺をなす頂点</param>
/// <param name="v2">辺をなす頂点</param>
/// <returns>点pが辺上に存在しているかどうか</returns>
/// <param name="p">Points to investigate.</param>
/// <param name="v1">Edge forming point.</param>
/// <param name="v2">Edge forming point.</param>
/// <returns>Whether a point exists on an edge.</returns>
public static bool ExistPointOnEdge(Vector3 p, Vector3 v1, Vector3 v2)
{
return 1 - TOLERANCE < Vector3.Dot((v2 - p).normalized, (v2 - v1).normalized);
}

/// <summary>
/// 点pが与えられた3点がなす三角形の辺上に存在するかを調査する
/// Investigate whether a point exists on a side of a triangle.
/// </summary>
/// <param name="p">調査点p</param>
/// <param name="t1">三角形をなす頂点</param>
/// <param name="t2">三角形をなす頂点</param>
/// <param name="t3">三角形をなす頂点</param>
/// <returns>点pが三角形の辺城に存在するかどうか</returns>
/// <param name="p">Points to investigate.</param>
/// <param name="t1">Vertex of triangle.</param>
/// <param name="t2">Vertex of triangle.</param>
/// <param name="t3">Vertex of triangle.</param>
/// <returns>Whether points lie on the sides of the triangle.</returns>
public static bool ExistPointOnTriangleEdge(Vector3 p, Vector3 t1, Vector3 t2, Vector3 t3)
{
if(ExistPointOnEdge(p, t1, t2) || ExistPointOnEdge(p, t2, t3) || ExistPointOnEdge(p, t3, t1))
Expand All @@ -61,14 +59,14 @@ public static bool ExistPointOnTriangleEdge(Vector3 p, Vector3 t1, Vector3 t2, V
}

/// <summary>
/// 点pが与えられた3点がなす三角形内部に存在するかを調査する
/// 入力(p, t1, t2, t3)各点は同一平面上に存在する必要がある
/// Investigate whether a point exists inside the triangle.
/// All points to be entered must be on the same plane.
/// </summary>
/// <param name="p">調査点p</param>
/// <param name="t1">三角形をなす頂点</param>
/// <param name="t2">三角形をなす頂点</param>
/// <param name="t3">三角形をなす頂点</param>
/// <returns>点pが三角形内部に存在するかどうか</returns>
/// <param name="p">Points to investigate.</param>
/// <param name="t1">Vertex of triangle.</param>
/// <param name="t2">Vertex of triangle.</param>
/// <param name="t3">Vertex of triangle.</param>
/// <returns>Whether the point exists inside the triangle.</returns>
public static bool ExistPointInTriangle(Vector3 p, Vector3 t1, Vector3 t2, Vector3 t3)
{
var a = Vector3.Cross(t1 - t3, p - t1).normalized;
Expand All @@ -84,50 +82,44 @@ public static bool ExistPointInTriangle(Vector3 p, Vector3 t1, Vector3 t2, Vecto
}

/// <summary>
/// 点pの三角形内におけるテクスチャ座標を計算する
/// 入力pは(t1, t2, t3)のなす三角形内部の点である必要がある
/// Calculate UV coordinates within a triangle of points.
/// The point to be investigated needs to be a point inside the triangle.
/// </summary>
/// <param name="p">調査点</param>
/// <param name="t1">三角形をなす頂点</param>
/// <param name="t1UV">t1が持つUV座標情報</param>
/// <param name="t2">三角形をなす頂点</param>
/// <param name="t2UV">t2が持つUV座標情報</param>
/// <param name="t3">三角形をなす頂点</param>
/// <param name="t3UV">t3が持つUV座標情報</param>
/// <param name="transformMatrix">入力(p, t1, t2, t3)各点をProjection-Spaceに変換する変換行列</param>
/// <returns>点pのテクスチャ座標</returns>
/// <param name="p">Points to investigate.</param>
/// <param name="t1">Vertex of triangle.</param>
/// <param name="t1UV">UV coordinates of t1.</param>
/// <param name="t2">Vertex of triangle.</param>
/// <param name="t2UV">UV coordinates of t2.</param>
/// <param name="t3">Vertex of triangle.</param>
/// <param name="t3UV">UV coordinates of t3.</param>
/// <param name="transformMatrix">MVP transformation matrix.</param>
/// <returns>UV coordinates of the point to be investigated.</returns>
public static Vector2 TextureCoordinateCalculation(Vector3 p, Vector3 t1, Vector2 t1UV, Vector3 t2, Vector2 t2UV, Vector3 t3, Vector2 t3UV, Matrix4x4 transformMatrix)
{
//各点をProjectionSpaceへの変換
Vector4 p1_p = transformMatrix * new Vector4(t1.x, t1.y, t1.z, 1);
Vector4 p2_p = transformMatrix * new Vector4(t2.x, t2.y, t2.z, 1);
Vector4 p3_p = transformMatrix * new Vector4(t3.x, t3.y, t3.z, 1);
Vector4 p_p = transformMatrix * new Vector4(p.x, p.y, p.z, 1);
//通常座標への変換(ProjectionSpace)
Vector2 p1_n = new Vector2(p1_p.x, p1_p.y) / p1_p.w;
Vector2 p2_n = new Vector2(p2_p.x, p2_p.y) / p2_p.w;
Vector2 p3_n = new Vector2(p3_p.x, p3_p.y) / p3_p.w;
Vector2 p_n = new Vector2(p_p.x, p_p.y) / p_p.w;
//頂点のなす三角形を点pにより3分割し、必要になる面積を計算
var s = 0.5f * ((p2_n.x - p1_n.x) * (p3_n.y - p1_n.y) - (p2_n.y - p1_n.y) * (p3_n.x - p1_n.x));
var s1 = 0.5f * ((p3_n.x - p_n.x) * (p1_n.y - p_n.y) - (p3_n.y - p_n.y) * (p1_n.x - p_n.x));
var s2 = 0.5f * ((p1_n.x - p_n.x) * (p2_n.y - p_n.y) - (p1_n.y - p_n.y) * (p2_n.x - p_n.x));
//面積比からuvを補間
var u = s1 / s;
var v = s2 / s;
var w = 1 / ((1 - u - v) * 1 / p1_p.w + u * 1 / p2_p.w + v * 1 / p3_p.w);
var uv = w * ((1 - u - v) * t1UV / p1_p.w + u * t2UV / p2_p.w + v * t3UV / p3_p.w);

return uv;
return w * ((1 - u - v) * t1UV / p1_p.w + u * t2UV / p2_p.w + v * t3UV / p3_p.w);
}

/// <summary>
/// 与えられた頂点/三角形リストから点pに一番近い頂点を持つ三角形の頂点リストを返す
/// Returns the vertex of the triangle with the closest vertex to the point to be examined from the given vertex and triangle list.
/// </summary>
/// <param name="p">調査点</param>
/// <param name="vertices">頂点リスト</param>
/// <param name="triangles">頂点の三角形リスト</param>
/// <returns></returns>
/// <param name="p">Points to investigate.</param>
/// <param name="vertices">Vertex list.</param>
/// <param name="triangles">Triangle list.</param>
/// <returns>The triangle closest to the point to be investigated.</returns>
public static Vector3[] GetNearestVerticesTriangle(Vector3 p, Vector3[] vertices, int[] triangles)
{
List<Vector3> ret = new List<Vector3>();
Expand Down Expand Up @@ -180,13 +172,13 @@ public static Vector3[] GetNearestVerticesTriangle(Vector3 p, Vector3[] vertices
}

/// <summary>
/// 点pを三角形空間内に投影した点を返す
/// Project points and return them inside the triangle.
/// </summary>
/// <param name="p">投影する点</param>
/// <param name="t1">三角形頂点</param>
/// <param name="t2">三角形頂点</param>
/// <param name="t3">三角形頂点</param>
/// <returns>投影後の三角形空間上の点</returns>
/// <param name="p">Point to project.</param>
/// <param name="t1">Vertex of triangle.</param>
/// <param name="t2">Vertex of triangle.</param>
/// <param name="t3">Vertex of triangle.</param>
/// <returns>Point inside the triangle after projection.</returns>
public static Vector3 TriangleSpaceProjection(Vector3 p, Vector3 t1, Vector3 t2, Vector3 t3)
{
var g = (t1 + t2 + t3) / 3;
Expand Down
29 changes: 9 additions & 20 deletions Assets/TexturePaint/Script/Core/MeshOperator.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -6,7 +6,7 @@
namespace Es.TexturePaint
{
/// <summary>
/// Mesh操作を行うクラス
/// A class that manipulates Mesh.
/// </summary>
public class MeshOperator
{
Expand All @@ -32,12 +32,12 @@ public MeshOperator(Mesh mesh)
}

/// <summary>
/// ローカル座標をUV座標に変換する
/// Convert local-space point to texture coordinates.
/// </summary>
/// <param name="localPoint">Local-Space Point</param>
/// <param name="matrixMVP">World-View-Projection変換行列</param>
/// <param name="uv">変換後のUV座標</param>
/// <returns>変換の成否</returns>
/// <param name="matrixMVP">World-View-Projection Transformation matrix.</param>
/// <param name="uv">UV coordinates after conversion.</param>
/// <returns>Whether the conversion was successful.</returns>
public bool LocalPointToUV(Vector3 localPoint, Matrix4x4 matrixMVP, out Vector2 uv)
{
int index0;
Expand All @@ -58,14 +58,11 @@ public bool LocalPointToUV(Vector3 localPoint, Matrix4x4 matrixMVP, out Vector2
t2 = meshVertices[meshTriangles[index1]];
t3 = meshVertices[meshTriangles[index2]];

//平面上に存在しない
if(!Math.ExistPointInPlane(p, t1, t2, t3))
continue;
//三角形の辺または内部に存在しない
if(!Math.ExistPointOnTriangleEdge(p, t1, t2, t3) && !Math.ExistPointInTriangle(p, t1, t2, t3))
continue;

//UV座標算出
var uv1 = meshUV[meshTriangles[index0]];
var uv2 = meshUV[meshTriangles[index1]];
var uv3 = meshUV[meshTriangles[index2]];
Expand All @@ -78,18 +75,14 @@ public bool LocalPointToUV(Vector3 localPoint, Matrix4x4 matrixMVP, out Vector2
}

/// <summary>
/// 指定したLocal-Space上の点に一番近いオブジェクト表面上の点を返す
/// Returns the point on the surface of Mesh closest to the point on the specified local-space.
/// </summary>
/// <param name="localPoint">Local-Space Point</param>
/// <returns>Local-Space Point</returns>
/// <param name="localPoint">The point of local-space.</param>
/// <returns>Mesh The point of local-space on the surface.</returns>
public Vector3 NearestLocalSurfacePoint(Vector3 localPoint)
{
var p = localPoint;

//頂点の中で一番近いものを含む三角形を取得
var tris = Math.GetNearestVerticesTriangle(p, meshVertices, meshTriangles);

//それぞれの三角形空間でそれっぽいp'を計算
var pds = new List<Vector3>();
for(int i = 0; i < tris.Length; i += 3)
{
Expand All @@ -98,11 +91,7 @@ public Vector3 NearestLocalSurfacePoint(Vector3 localPoint)
var i2 = i + 2;
pds.Add(Math.TriangleSpaceProjection(p, tris[i0], tris[i1], tris[i2]));
}

//pに一番近いp'が求めたかったオブジェクト表面
var pd = pds.OrderBy(t => Vector3.Distance(p, t)).First();

return pd;
return pds.OrderBy(t => Vector3.Distance(p, t)).First();
}

#endregion PublicMethod
Expand Down
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