消隱的實現

消隱的實現

原創

2020-02-21 04:48

最近做了個圖形學的大作業。一開始還不知道怎麼把一個三維存儲的圖形呈現到平面內，一天內，確實只有一天內就完成了基本的投影和消隱算法，頗有成就感！

其實在投影上作了很大的簡化，僅僅把圖像投影到xy平面，可想有多簡單了吧~取xy座標值即可。

消隱的實現還是破費周折的，主要步驟是：計算平面上凸包，凸包上的點標記爲邊界點；與邊界點相連的點，通過向量的計算確定是可見內點還是不可見內點；最後遞歸的把可見內點的相鄰點標爲可見點，不可見內點的相鄰點標爲不可見點；任意線段根據兩端的端點類型（可見內點、不可見內點、邊界點）標識線段是否可見。

消隱的代碼如下：

private void HideLines(Graphics g)
        {
            int i;
            for (i = 0; i < Points.Count; ++i)
                ((_3DPoint)Points[i]).type = 0;

ArrayList EdgePoints = new ArrayList();
            GetEdges(EdgePoints);
            //for (i = 0; i < EdgePoints.Count-1; ++i)

// g.DrawString(i + " ", new Font("Arial", 20), Brushes.Blue, new PointF(((_3DPoint)EdgePoints[i]).X, ((_3DPoint)EdgePoints[i]).Y));

for (i = 1; i < EdgePoints.Count - 1; ++i)
            {
                _3DPoint vector1 = (_3DPoint)EdgePoints[i - 1] - (_3DPoint)EdgePoints[i],
                    vector2 = (_3DPoint)EdgePoints[i + 1] - (_3DPoint)EdgePoints[i];
                for (int j = 0; j < Points.Count; ++j)
                {
                    _3DPoint p = (_3DPoint)Points[j];
                    if (p.type != 0)
                        continue;
                    int index = Lines.IndexOf(new _3DLine(p, (_3DPoint)EdgePoints[i]));
                    if (index == -1)
                        continue;
                    _3DPoint vector3 = p - (_3DPoint)EdgePoints[i];
                    double test = vector1.CrossProduct(vector2).DotProduct(vector3);
                    if (test.CompareTo(0.0) > 0)
                        p.type = 2;
                    else if (test.CompareTo(0.0) < 0)
                        p.type = -1;
                }
            }
            Queue q = new Queue();
            for (i = 0; i < Points.Count; ++i)
            {
                _3DPoint p = (_3DPoint)Points[i];
                if (p.type == 2 || p.type == -1)
                    q.Enqueue(p);
            }
            while (q.Count > 0)
            {
                _3DPoint p = (_3DPoint)q.Dequeue();
                for (int j = 0; j < Points.Count; ++j)
                {
                    _3DPoint p1 = (_3DPoint)Points[j];
                    if (p1.type != 0)
                        continue;
                    if (Lines.IndexOf(new _3DLine(p, p1)) >= 0)
                    {
                        p1.type = p.type;
                        q.Enqueue(p1);
                    }
                }
            }

//for (i = 0; i < Points.Count; ++i)

//{

// _3DPoint p = (_3DPoint)Points[i];

// g.DrawString(p.type + " ", new Font("Arial", 20), Brushes.Blue, new PointF(p.X, p.Y));

//}

for (i = 0; i < Lines.Count; ++i)
            {
                _3DLine l = (_3DLine)Lines[i];
                int t1 = l.Vertex1.type, t2 = l.Vertex2.type;
                if (t1 == 2 || t2 == 2)
                {
                    l.Visible = true;
                    continue;
                }
                else if (t1 == -1 || t2 == -1)
                {
                    l.Visible = false;
                    continue;
                }
                else
                    l.Visible = true;
            }
        }

private void GetEdges(ArrayList ps)
        {
            int i ;

_3DPoint topest = (_3DPoint)Points[0];
            for (i = 1; i < Points.Count; ++i)
            {
                if (((_3DPoint)Points[i]).Y > topest.Y)
                    topest = (_3DPoint)Points[i];
            }
            ps.Add(topest);
            topest.type = 1;

_3DPoint nextEdge = topest, candidate, p;
            double minAngle, lastAngle = -2 * Math.PI-1, angle;
            while (true)
            {
                minAngle = 2 * Math.PI + 1;
                candidate = null;
                for (i = 0; i < Points.Count; ++i)
                {
                    p = (_3DPoint)Points[i];
                    if (p == nextEdge || (p.type == 1 && p != topest))
                        continue;
                    angle = Math.Atan2(p.Y - nextEdge.Y, p.X - nextEdge.X);
                    if (angle > lastAngle && angle < minAngle)
                    {
                        candidate = p;
                        minAngle = angle;
                    }
                }
                if (candidate == null) break;
                lastAngle = Math.Atan2(candidate.Y - nextEdge.Y, candidate.X - nextEdge.X);
                candidate.type = 1;
                nextEdge = candidate;
                ps.Add(candidate);
                if (nextEdge == topest) break;
            }
            ps.Add((_3DPoint)ps[1]);
        }

效果頗爲滿意，上傳個截圖：