graphmath.pas

这是图形处理中常用的数学计算方法。比较全面

{**************************************************************}
{                                                              }
{  图形数学函数库, 提供非常有用的图形运算方法。   　           }
{  ( 过教学反复测试)                                           }
{                                                              }
{**************************************************************}

unit GraphMath;

interface

uses
  Windows,  SysUtils, Classes, Graphics, Math, Variants;   

const
  NULL_VALUE = MaxInt;
  ERR_SLOPE = MaxInt;           //不存在的斜率
  InError: Double = 1.0E-7;
  ERROR9 = 1.0E-9;
  ERROR8 = 1.0E-8;
  ERROR7 = 1.0E-7;
  ERROR4 = 1.0E-4;
  ERROR2 = 0.00872664625997;    //0.5度对应的弧度值

  PI34 = 3 * Pi / 4;
  PI14 = pi / 4;
  PI12 = pi / 2;
  PI32 = 3 * pi / 2;

type

  TObjectType = (otUnknown, otLine, otPolygon, otArc, otCircle, otRect, otText, otCross, otGroup);

  TArcCase = (acPtSmall, acPtBig, acCSmall, acCBig, acNotCSmall, acNotCBig);

  TMyPosition = (psUnknown, psLeft, psTop, psRight, psBottom);
  TPointLinePos = (plUnknown, plOn, plLeft, plTop, plRight, plBottom); 

  {R1在R2的内部(rpIn); 1：相交(rpCross) 2：相离(rpOut) 3:重叠(rpOver) 4: R1包含R2(rpBein)}
  TRectPosition = (rpUnknown, rpIn, rpBeIn, rpOver, rpCross, rpOut);

  {多边形边的关系：不确定，部分重复，相交，相切，相离，一边端点在另一边上}
  TDotPolyPos = (dpUnknown, dpOn, dpIn, dpOut);
  TEdgeEdgePos = (eeUnknown, eePartRep, eeCross, eeCut, eeOff, eeFirstOnSec, eeSecOnFirst);
  TEdgePolyPos = (epUnknown,  epOutAdj, epInAdj, epCross, epIn, epOut);

  TLongStr = string[32];    //长名称字符串
  TShortStr = string[10];   //短名称字符串
  TNameStr = string[20];    //图形名称字符串

{ 角度 }

  TDegree = Double;
  TRadian = Double;

{一元二次方程的根}

  TEquationRadix = record
    x1, x2: Double;        //根值
    RadixNum: ShortInt;    //0:无根；1:1个根；2:2个根
  end;

{ 坐标点}

  pRealPoint = ^TRealPoint;
  TRealPoint = record
    x, y: Double;
  end;

{ 交点 }

  TCrossPoint = record
    PointNum: ShortInt;            //PointNum = 0:无交点；1:1个交点；2:2个交点 
    IsCutPoint: Boolean;           //弧线、弧弧是否相切, 在返回的PointNum＝1时才有意义
    case Byte of
      0: (x1, y1, x2, y2: Double); //第一交点, 第二交点
      1: (P1, P2: TRealPoint);
  end; 

  TRealLine = record 
    x1, y1, x2, y2: Double;
  end;

{ 直线（斜截式）}

  TBeeLine = record
    k: Double;       //斜率
    b: Double;       //截距
    ExistK: Boolean; //是否有斜率(若无斜率，b=x)
  end;

{ 线段（两点式）}

  TSecLine = record
    case Byte of
      0: (x1, y1, x2, y2: Double);
      1: (P1, P2: TRealPoint);
  end;

{ 标准矩形 }

  TRectangle = record
    case Byte of
      0: (Left, Top, Right, Bottom: Double);
      1: (TopLeft, BottomRight: TRealPoint);
  end;

  TBox = record
    minx, miny, maxx, maxy: double;
  end;

  TIntRect = record
    case Byte of
      0: (x1, y1, x2, y2, x3, y3, x4, y4: Integer); //Order Four Points?
      1: (Point1, Point2, Point3, Point4: TPoint);
  end;

{任意矩形}

  TAnyRectangle = record
    case Byte of
      0: (x1, y1, x2, y2, x3, y3, x4, y4: Double); // 左上，右上，右下，左下
      1: (Point1, Point2, Point3, Point4: TRealPoint);
  end;

{ 圆}

  TCircle = record
    cx, cy: Double; //圆心
    r: Double;      //半径
  end;

{ 弧线（三点式）}

  TPointArc = record
    case Byte of
      0: (x1, y1, x2, y2, x3, y3: Double); //端点一,端点二,端点三
      1: (P1, P2, P3: TRealPoint);
  end;

{ 弧线（圆心式）}   

  TCircleArc = record 
    sAng, eAng: TRadian; //起始、终止角[0..2*pi)
    R: Double;           //半径
    line: Double;
    ClockWise: Boolean; //标记弧形的顺逆时针方向，为真表示为顺时针 
    case Integer of
      0: (ox, oy, sx, sy, ex, ey: Double); //圆心坐标
      1: (oPnt, sPnt, ePnt: TRealPoint);
  end;

{ 环形 }

  PAnnular = ^TAnnular;
  TAnnular = record
    ox, oy: Double;         // 圆心点
    sAng, eAng: Double;     // 起始角，终止角
    r1, r2: Double;         // 内弧半径,外弧半径
  end;


{ 边弧 }

  pPolygonArc = ^TPolygonArc;
  TPolygonArc = record
    sAng, eAng: TRadian;    //圆心角(Img顺，Math逆)[0..2pi);
    R: Double;              //弧半径
    bOutFlag: Boolean;      //凹凸
    case Byte of
      0: (Ox, Oy: Double);  //弧圆心
      1: (OPnt: TRealPoint);
  end;

{ 边 }

  PPolygonEdge = ^TPolygonEdge;
  TPolygonEdge = record
    pPolyArc: pPolygonArc;         //弧域，nil表示非弧边
    pEdgePrior: PPolygonEdge;      //前一条边(缺省为nil，头结点的pEdgePrior指向尾结点)
    pEdgeNext: PPolygonEdge;       //多边形下一条边(缺省为nil)
    pReserve: Pointer;             //保留指针
    Tag: Integer;                  //边附加标记
    case Byte of
      0: (sX, sY, eX, eY: Double); //边(包括弧边)的端点
      1: (sPnt, ePnt: TRealPoint);
  end;

{ 多边形 }

  pPolygonRecord = ^TPolygonRecord;
  TPolygonRecord = record
    pHeadEdge: PPolygonEdge; //第一条边
    EdgeCount: Integer;      //边数
    BoxRect: TRectangle;     //外围矩形
    bExistArc: Boolean;      //是否存在弧边
    pOther: Pointer;         //保留的指针
    Name: string[20];        //多边形名
  end;

{ 矩形 }

  pRectRecord = ^TRectRecord;
  TRectRecord = record
    Rect: TRectangle;
    BoxRect: TRectangle;     //外围矩形
    LineWidth: Double;       //线宽
    Name: string[20];
  end;

{ 弧形 }

  pArcRecord = ^TArcRecord;
  TArcRecord = record
    pArcData: pPolygonArc;
    BoxRect: TRectangle;     //外围矩形
    ArcWidth: Double;        //弧宽
    Name: string[20];
    case Byte of
      0: (sX, sY, eX, eY: Double); //边(包括弧边)的端点
      1: (sPnt, ePnt: TRealPoint);
  end;

{ 圆 }

  pCircleRecord = ^TCircleRecord;
  TCircleRecord = record
    R: Double;       //圆心半径
    BoxRect: TRectangle;     //外围矩形
    LineWidth: Double;       //弧宽
    Name: string[20];
    case Byte of
      0: (oX, oY: Double);
      1: (oPnt: TRealPoint);
  end;

{ 线段 }

  pLineRecord = ^TLineRecord;
  TLineRecord = record
    Line: TSecLine;          //线段
    BoxRect: TRectangle;     //外围矩形
    LineWidth: Double;       //弧宽
    Name: string[20];
  end;

{ 文本 }

  pTextRecord = ^TTextRecord;
  TTextRecord = record
    Text: string;
    Color: TColor;
    BkColor: TColor;
    BoxRect: TRectangle;
    Angle: Double;
    Name: string;
  end;

{ 图形对象 }

  pObjRec = ^TObjRec;
  TObjRec = record
    shape: TObjectType;
    pObj: Pointer;
    BoxRect: TRectangle; 
    bVisible: Boolean;
    bSelected: Boolean;
    bDeleted: Boolean;
  end;

{ 数组类型 }

  TArr33 = array[1..3, 1..3] of Extended;
  TArr1 = array[1..3] of Extended;
  TListArray = array of TList;
  TPointArray = array of TPoint;
  TRealPointArray = array of TRealPoint;


//===========================基本计算方法=====================================================>>

{加法运算}
procedure Add(var x: Integer; n: Integer); overload;
procedure Add(var x: Double; n: Double); overload;
procedure Add(var s1: string; s2: string); overload;

{减法运算}
procedure Sub(var x: Integer; n: Integer); overload;
procedure Sub(var x: Double; n: Double); overload;
procedure Sub(var s1: string; s2: string); overload;

{矢量减}
function VectorMinus(const dPnt1, dPnt2: TRealPoint): TRealPoint;

{矢量叉积}
function VectorCrossMult(const dPnt1, dPnt2: TRealPoint; Err: Double = ERROR7): Double;

{交换值}
procedure SwapValue(var x1, x2: Double); OverLoad;
procedure SwapValue(var x1, x2: Integer); OverLoad;
procedure SwapValue(var d1, d2: TRealPoint); OverLoad;
procedure SwapValue(var L1, L2: TLineRecord); OverLoad;
procedure SwapValue(var p1, p2: pointer); OverLoad;
procedure SwapValue(var List: TList; I, J: Integer); OverLoad;

{排序}
procedure MaxToMin(var x1, x2: Double);
procedure MinToMax(var x1, x2: Double);

{最大最小值}
function MaxV(const x1, x2: Integer): Integer; OverLoad;
function MaxV(const x1, x2: Double): Double; OverLoad;
function MaxV(const x1, x2, x3: Integer): Integer; OverLoad;
function MaxV(const x1, x2, x3: Double): Double; OverLoad;
function MinV(const x1, x2: Integer): Integer; OverLoad;
function MinV(const x1, x2: Double): Double; OverLoad;
function MinV(const x1, x2, x3: Integer): Integer; OverLoad;
function MinV(const x1, x2, x3: Double): Double; OverLoad;

{矩阵乘积}
function MatrixMultiply(const T1, T2: TArr33): TArr33;

{计算一元二次方程的根}
function EquationRadix(a, b, c: Double): TEquationRadix;

{将角度调整到[0,2*pi)}
function NormalDegree(const Angle: TDegree): TDegree;
function NormalRadian(const Radian: TRadian): TRadian;

{求正弦,余弦}
function MyCos(Angle: TRadian): Double;
function MySin(Angle: TRadian): Double;

{点的数组排序(从小到大)}
procedure SortPointByX(var dPntsArr: TRealPointArray); //按照x坐标
procedure SortPointByY(var dPntsArr: TRealPointArray); //按照y坐标
procedure SortPoint(var dPntsArr: TRealPointArray); //如果X坐标不同，按X排序，否则按Y排序
procedure SortArcPoint(var dPntsArr: TRealPointArray; OPnt: TRealPoint; R: Double); //对弧上的一些点排序（按照弧度从小到大）

//==========================判断类===============================================================>>

{比较实数大小关系R:实数;E:等于;L:小于;G:大于;}
function RE(const a, b: Double; Err: Double = ERROR7): Boolean;
function RL(const a, b: Double; Err: Double = ERROR7): Boolean;
function RG(const a, b: Double; Err: Double = ERROR7): Boolean;
function RLE(const a, b: Double; Err: Double = ERROR7): Boolean;
function RGE(const a, b: Double; Err: Double = ERROR7): Boolean;

{两个变量是否相同}
function VarEqual(const A, B: Variant): Boolean;

{两点是否相同}
function IsSamePoint(const x1, y1, x2, y2: Double; Err: Double = ERROR7): Boolean; overload;
function IsSamePoint(const Pnt1, Pnt2: TRealPoint; Err: Double = ERROR7): Boolean; overload;

{两边是否相同数据}
function IsSameEdge(const pEdge1, pEdge2: pPolygonEdge; Err: Double = ERROR7): Boolean;

{两个多边形是否完全一样（重叠）}
function IsSamePolygon(const pPolygon1, pPolygon2: pPolygonRecord; Err: Double = ERROR7): Boolean;

{一个角是否在另两个角之间}
function BetweenAngle(Ang, Ang1, Ang2: TRadian; Err: Double = ERROR7): Boolean;

{一值是否在另两值之间}
function BetweenValue(const Val, Val1, Val2: Double; Err: Double = ERROR7): Boolean;

{点是否在直线上}
function PointOnLine(const x, y: Double; const BLine: TBeeLine; Err: Double = ERROR7): Boolean; overload;
function PointOnLine(const x, y: Double; const BLine: TSecLine; Err: Double = ERROR7): Boolean; overload;
function PointOnLine(const Pnt, Pnt1, Pnt2: TRealPoint; Err: Double = ERROR7): Boolean; overload;
function PointOnLine(const Pnt: TRealPoint; pEdge: pPolygonEdge; Err: Double = ERROR7): Boolean; overload;