PCB 板边倒圆角的实现方法（基本算法一）
当PCB外形是直角时,一般工程制做外形(锣带）时,会将直角或尖角的地方倒成圆角，主要是为了防止PCB容易划伤板他扎伤人html
因此当客户没有特殊要求时,PCB外形是直角通常会默认倒角0.5mm圆角(以下图所示)算法
一.PCB板边倒圆角点分析
原PCB外形 以下图图示:看了这个PCB外形,产生有2个问题点.数据结构
1.外形中哪些点需倒圆角?ide
2.如何怎么倒圆角?this
1.外形中哪些点需倒圆角?spa
看下图: PCB外形倒圆角的点,恰好就是咱们凸包需求出的点,接下来咱们将玩转凸包了,只要求出凸包，那么就能够实现PCB板边倒圆角啦。code
求凸包的算法：咱们能够借鉴算法导论中的查找凸包的算法（加以改进获得新的求凸包方法，详见【方法一】与【方法二】）htm
2.如何怎么倒圆角?blog
在下面有说明倒角方法.排序
二. 求凸点
方法一求凸点:【采用多轮遍历,一遍一遍将凹点踢除，剩于的便是凸点】
方法一求凸点: 代码
/// <summary> /// 求最大多边形最大凸包1 【采用多轮遍历将凹点踢除，剩于的便是凸点】 /// </summary> /// <param name="gSur_Point_list"></param> /// <returns></returns> public List<gSur_Point> s_convex_polyon1(List<gSur_Point> gSur_Point_list) { add addCOM = new add(); bool isOK = true; List<gSur_Point> PointList = new List<gSur_Point>(); var isCCW = s_isCCW(gSur_Point_list); int sum = gSur_Point_list.Count() - 1; int n = gSur_Point_list.Count(); for (int i = 0; i < n; i++) { int IndexPre = (i - 1) % sum; if (IndexPre == -1) IndexPre = sum - 1; int IndexCurrent = i % sum; int IndexNext = (i + 1) % sum; if (gSur_Point_list[IndexPre].type_point > 0) continue; if (gSur_Point_list[IndexCurrent].type_point > 0) continue; var multiVal = multi(gSur_Point_list[IndexPre].p, gSur_Point_list[IndexCurrent].p, gSur_Point_list[IndexNext].p); if ((isCCW && multiVal > 0) || (!isCCW && multiVal < 0)) PointList.Add(gSur_Point_list[IndexCurrent]); else isOK = false; } List<gSur_Point> Point2List = new List<gSur_Point>(PointList); while (!isOK) { isOK = true; PointList.Clear(); PointList.AddRange(Point2List); Point2List.Clear(); sum = PointList.Count() - 1; n = PointList.Count(); for (int i = 0; i < n; i++) { int IndexPre = (i - 1) % sum; if (IndexPre == -1) IndexPre = sum - 1; int IndexCurrent = i % sum; int IndexNext = (i + 1) % sum; var multiVal = multi(PointList[IndexPre].p, PointList[IndexCurrent].p, PointList[IndexNext].p); if ((isCCW && multiVal > 0) || (!isCCW && multiVal < 0)) Point2List.Add(PointList[IndexCurrent]); else isOK = false; } } return Point2List; }
方法二求凸包：【采用一边遍历找出凸点并加入队列，并同时将队列中的凸点队列中找出凹点踢除】
方法二求凸包代码:
/// <summary> /// 求最大多边形最大凸包2 【采用一边遍历找出凸点并加入队列，并同时将队列中的凸点队列中找出凹点踢除】 /// </summary> /// <param name="gSur_Point_list"></param> /// <returns></returns> public List<gSur_Point> s_convex_polyon2(List<gSur_Point> gSur_Point_list) { Stack<gSur_Point> StackPoint = new Stack<gSur_Point>(); var isCCW = s_isCCW(gSur_Point_list); int sum = gSur_Point_list.Count() - 1; int n = gSur_Point_list.Count(); for (int i = 0; i < n; i++) { int IndexPre = (i - 1) % sum; if (IndexPre == -1) IndexPre = sum - 1; int IndexCurrent = i % sum; int IndexNext = (i + 1) % sum; if (gSur_Point_list[IndexPre].type_point > 0) continue; if (gSur_Point_list[IndexCurrent].type_point > 0) continue; var multiVal = multi(gSur_Point_list[IndexPre].p, gSur_Point_list[IndexCurrent].p, gSur_Point_list[IndexNext].p); if ((isCCW && multiVal > 0) || (!isCCW && multiVal < 0)) { L1: if (StackPoint.Count > 1) { var Top1Point = StackPoint.Pop(); var Top2Point = StackPoint.Peek(); multiVal = multi(Top2Point.p, Top1Point.p, gSur_Point_list[IndexCurrent].p); if ((isCCW && multiVal > 0) || (!isCCW && multiVal < 0)) StackPoint.Push(Top1Point); else goto L1; } StackPoint.Push(gSur_Point_list[IndexCurrent]); } } return StackPoint.Reverse().ToList(); }
方法三求凸包:【按算法导论Graham扫描法 各节点按方位角+距离 逆时针排序 依次检查,当不属凸点于则弹出】
方法三求凸包代码
/// <summary> /// 求最大多边形最大凸包5 【按算法导论Graham扫描法 各节点按方位角+距离 逆时针排序 依次检查,当不属凸点于则弹出】 /// 因为把各点的排列顺序从新排序了，只支持折线节点(当存在弧节点时会出异常 ！！！) /// </summary> /// <param name="gSur_Point_list"></param> /// <returns></returns> public List<gSur_Point> s_convex_polyon3(List<gSur_Point> gSur_Point_list) { var LeftBottomPoint = gSur_Point_list.OrderBy(tt => tt.p.y).ThenBy(tt => tt.p.x).FirstOrDefault(); gSur_Point_list.RemoveAt(gSur_Point_list.Count - 1); gSur_Point_list.ForEach(tt => { tt.Value = p2p_di(LeftBottomPoint.p, tt.p); tt.Angle = p_ang(LeftBottomPoint.p, tt.p); } ); gSur_Point_list = gSur_Point_list.OrderBy(tt => tt.Angle).ThenBy(tt => tt.Value).ToList(); gSur_Point_list.Add(gSur_Point_list[0]); Stack<gSur_Point> StackPoint = new Stack<gSur_Point>(); var isCCW = true; int sum = gSur_Point_list.Count() - 1; int n = gSur_Point_list.Count(); for (int i = 0; i < n; i++) { int IndexPre = (i - 1) % sum; if (IndexPre == -1) IndexPre = sum - 1; int IndexCurrent = i % sum; int IndexNext = (i + 1) % sum; var multiVal = multi(gSur_Point_list[IndexPre].p, gSur_Point_list[IndexCurrent].p, gSur_Point_list[IndexNext].p); if (isCCW && multiVal > 0) { L1: if (StackPoint.Count > 1) { var Top1Point = StackPoint.Pop(); var Top2Point = StackPoint.Peek(); multiVal = multi(Top2Point.p, Top1Point.p, gSur_Point_list[IndexCurrent].p); if (isCCW && multiVal > 0) StackPoint.Push(Top1Point); else goto L1; } StackPoint.Push(gSur_Point_list[IndexCurrent]); } } return StackPoint.Reverse().ToList(); }
公共方法与数据结构
/// <summary> /// Surface 坐标泛型集类1 /// </summary> public class gSur_Point { public gSur_Point() { } public gSur_Point(double x_val, double y_val, byte type_point_) { this.p.x = x_val; this.p.y = y_val; this.type_point = type_point_; } public gSur_Point(gPoint p, byte type_point_) { this.p = p; this.type_point = type_point_; } public gPoint p; /// <summary> /// 0为折点 1为顺时针 2为逆时针 /// </summary> public byte type_point { get; set; } = 0; /// <summary> /// 值 /// </summary> public double Value { get; set; } = 0; /// <summary> /// 角度 /// </summary> public double Angle { get; set; } = 0; /// <summary> /// 标记 /// </summary> public bool isFalg { get; set; } } /// <summary> /// 点 数据类型 (XY) /// </summary> public struct gPoint { public gPoint(gPoint p_) { this.x = p_.x; this.y = p_.y; } public gPoint(double x_val, double y_val) { this.x = x_val; this.y = y_val; } public double x; public double y; public static gPoint operator +(gPoint p1, gPoint p2) { p1.x += p2.x; p1.y += p2.y; return p1; } public static gPoint operator -(gPoint p1, gPoint p2) { p1.x -= p2.x; p1.y -= p2.y; return p1; } public static gPoint operator +(gPoint p1, double val) { p1.x += val; p1.y += val; return p1; } public static bool operator ==(gPoint p1, gPoint p2) { return (p1.x == p2.x && p1.y == p2.y); } public static bool operator !=(gPoint p1, gPoint p2) { return !(p1.x == p2.x && p1.y == p2.y); } } /// <summary> /// 求叉积 判断【点P与线L】位置关系【小于0】在右边 【大于0】在左边 【等于0】共线 /// </summary> /// <param name="ps"></param> /// <param name="pe"></param> /// <param name="p"></param> /// <returns>【小于0】在右边 【大于0】在左边 【等于0】共线</returns> public double multi(gPoint ps, gPoint pe, gPoint p) { return ((ps.x - p.x) * (pe.y - p.y) - (pe.x - p.x) * (ps.y - p.y)); } /// <summary> /// 检测 Surface是否逆时针 /// </summary> /// <param name="gSur_Point_list"></param> /// <returns></returns> public bool s_isCCW(List<gSur_Point> gSur_Point_list) { double d = 0; int n = gSur_Point_list.Count() - 1; for (int i = 0; i < n; i++) { if (gSur_Point_list[i].type_point > 0) continue; int NextI = i + 1 + (gSur_Point_list[i + 1].type_point > 0 ? 1 : 0); d += -0.5 * (gSur_Point_list[NextI].p.y + gSur_Point_list[i].p.y) * (gSur_Point_list[NextI].p.x - gSur_Point_list[i].p.x); } return d > 0; } /// <summary> /// 返回两点之间欧氏距离 /// </summary> /// <param name="p1"></param> /// <param name="p2"></param> /// <returns></returns> public double p2p_di(gPoint p1, gPoint p2) { return Math.Sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y)); } /// <summary> /// 求方位角 /// </summary> /// <param name="ps"></param> /// <param name="pe"></param> /// <returns></returns> public double p_ang(gPoint ps, gPoint pe) { double a_ang = Math.Atan((pe.y - ps.y) / (pe.x - ps.x)) / Math.PI * 180; //象限角 转方位角 计算所属象限 并求得方位角 if (pe.x >= ps.x && pe.y >= ps.y) //↗ 第一象限 { return a_ang; } else if (!(pe.x >= ps.x) && pe.y >= ps.y) // ↖ 第二象限 { return a_ang + 180; } else if (!(pe.x >= ps.x) && !(pe.y >= ps.y)) //↙ 第三象限 { return a_ang + 180; } else if (pe.x >= ps.x && !(pe.y >= ps.y)) // ↘ 第四象限 { return a_ang + 360; } else { return a_ang; } }
三.板边凸点倒圆角方法
方法一.也最简单的倒角方法,咱们将PCB板边凸点找出来后，能够直接借助genesis倒角功能就能够实现了
固然但偶尔会报错的, 且当N个小线段组成的尖角倒角会出错(要实现完美效果只有本身写倒角算法啦)
方法二:本身写倒角算法，这个算法和加内角孔算法相似（这里只是介绍简单的倒角)考虑特殊的须要扩展
能够参考这篇文章: http://www.noobyard.com/article/p-yrygtefj-bm.html
四.凸点加倒圆角实现效果