Добавил третью главу занимательного программирования
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344
Занимательное программирование/3/5_ideal_gas/geometry.pas
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344
Занимательное программирование/3/5_ideal_gas/geometry.pas
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unit Geometry;
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{$mode ObjFPC}{$H+}
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interface
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uses
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Classes, SysUtils;
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type
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{ Вершины }
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Vertex = record
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x, y, z: Real; { Координаты вершины }
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end;
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{ Ребра }
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Edge = record
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src, dest: Integer; { Индексы соединяемых вершин }
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end;
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Object3D = class
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public
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vertices: array of Vertex; { вершины }
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edges: array of Edge; { ребра }
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xc, yc, zc: Real; { координаты центра объекта }
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vx, vy, vz: Real; { значения составляющих его скорости }
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xa, ya, za: Real; { скорость вращения вокруг оси }
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constructor Create(var center, velocity, axis: Vertex);
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procedure MoveCenter();
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end;
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Matrix = array[1..4, 1..4] of Real; { матрица 4x4 }
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Column = array[1..4] of Real; { столбец }
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function CopyObject3D(Shape: Object3D): Object3D;
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{ умножение матрицы на матрицу }
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function MMMult(lhs, rhs: Matrix): Matrix;
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{ умножение матрицы на столбец }
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function MCMult(lhs: Matrix; rhs: Column): Column;
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{ матрица поворота модели }
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function RotateMatrix(xa, ya, za: Real): Matrix;
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function MoveMatrix(tx, ty, tz: Real): Matrix;
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function ResizeMatrix(sx, sy, sz: Real): Matrix;
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procedure RotateShape(Shape: Object3D);
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procedure MoveShape(Shape: Object3D; Width, Height: Real);
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procedure ResizeShape(var Shape: Object3D; sx, sy, sz: Real);
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implementation
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constructor Object3D.Create(var center, velocity, axis: Vertex);
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const
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size = 10;
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cubeVertices: array of Vertex = (
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(x: -size; y: -size; z: -size),
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(x: -size; y: size; z: -size),
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(x: size; y: size; z: -size),
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(x: size; y: -size; z: -size),
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(x: -size; y: -size; z: size),
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(x: -size; y: size; z: size),
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(x: size; y: size; z: size),
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(x: size; y: -size; z: size)
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);
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cubeEdges: array of Edge = (
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(src: 0; dest: 1),
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(src: 1; dest: 2),
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(src: 2; dest: 3),
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(src: 3; dest: 0),
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(src: 4; dest: 5),
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(src: 5; dest: 6),
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(src: 6; dest: 7),
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(src: 7; dest: 4),
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(src: 0; dest: 4),
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(src: 1; dest: 5),
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(src: 2; dest: 6),
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(src: 3; dest: 7)
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);
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begin
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vertices := cubeVertices;
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edges := cubeEdges;
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xc := center.x;
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yc := center.y;
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zc := center.z;
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vx := velocity.x;
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vy := velocity.y;
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vz := velocity.z;
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xa := axis.x;
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ya := axis.y;
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za := axis.z
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end;
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procedure Object3D.MoveCenter();
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begin
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xc := xc + Vx;
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yc := yc + Vy;
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zc := zc + Vz
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end;
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function CopyObject3D(Shape: Object3D): Object3D;
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begin
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CopyObject3D.vertices := Copy(Shape.vertices, 0);
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CopyObject3D.edges := Copy(Shape.edges, 0);
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CopyObject3D.xc := Shape.xc;
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CopyObject3D.yc := Shape.yc;
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CopyObject3D.zc := Shape.zc
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end;
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function MMMult(lhs, rhs: Matrix): Matrix;
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var
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i, j, k: Integer;
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r: Matrix;
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s: Real;
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begin
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for i := 1 to 4 do
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for j := 1 to 4 do
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begin
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s := 0;
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for k := 1 to 4 do
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s := s + lhs[i, k] * rhs[k, j];
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r[i, j] := s;
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end;
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MMMult := r;
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end;
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function MCMult(lhs: Matrix; rhs: Column): Column;
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var
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k, i: Integer;
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s: Real;
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r: Column;
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begin
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for i := 1 to 4 do { аналогично MMMult }
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begin
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s := 0;
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for k := 1 to 4 do
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s := s + lhs[i, k] * rhs[k];
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r[i] := s;
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end;
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MCMult := r;
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end;
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function RotateMatrix(xa, ya, za: Real): Matrix;
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var
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xr, yr, zr: Matrix;
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begin
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{ матрица поворота вокруг оси Ox }
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xr[1, 1] := 1;
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xr[1, 2] := 0;
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xr[1, 3] := 0;
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xr[1, 4] := 0;
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xr[2, 1] := 0;
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xr[2, 2] := Cos(xa);
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xr[2, 3] := -Sin(xa);
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xr[2, 4] := 0;
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xr[3, 1] := 0;
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xr[3, 2] := Sin(xa);
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xr[3, 3] := Cos(xa);
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xr[3, 4] := 0;
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xr[4, 1] := 0;
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xr[4, 2] := 0;
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xr[4, 3] := 0;
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xr[4, 4] := 1;
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{ матрица поворота вокруг оси Oy }
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yr[1, 1] := Cos(ya);
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yr[1, 2] := 0;
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yr[1, 3] := Sin(ya);
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yr[1, 4] := 0;
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yr[2, 1] := 0;
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yr[2, 2] := 1;
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yr[2, 3] := 0;
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yr[2, 4] := 0;
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yr[3, 1] := -Sin(ya);
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yr[3, 2] := 0;
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yr[3, 3] := Cos(ya);
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yr[3, 4] := 0;
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yr[4, 1] := 0;
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yr[4, 2] := 0;
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yr[4, 3] := 0;
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yr[4, 4] := 1;
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{ матрица поворота вокруг оси Oz }
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zr[1, 1] := Cos(za);
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zr[1, 2] := -Sin(za);
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zr[1, 3] := 0;
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zr[1, 4] := 0;
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zr[2, 1] := Sin(za);
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zr[2, 2] := Cos(za);
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zr[2, 3] := 0;
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zr[2, 4] := 0;
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zr[3, 1] := 0;
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zr[3, 2] := 0;
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zr[3, 3] := 1;
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zr[3, 4] := 0;
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zr[4, 1] := 0;
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zr[4, 2] := 0;
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zr[4, 3] := 0;
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zr[4, 4] := 1;
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RotateMatrix := MMMult(MMMult(xr, yr), zr)
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end;
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function MoveMatrix(tx, ty, tz: Real): Matrix;
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begin
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MoveMatrix[1, 1] := 1;
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MoveMatrix[1, 2] := 0;
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MoveMatrix[1, 3] := 0;
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MoveMatrix[1, 4] := tx;
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MoveMatrix[2, 1] := 0;
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MoveMatrix[2, 2] := 1;
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MoveMatrix[2, 3] := 0;
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MoveMatrix[2, 4] := ty;
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MoveMatrix[3, 1] := 0;
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MoveMatrix[3, 2] := 0;
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MoveMatrix[3, 3] := 1;
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MoveMatrix[3, 4] := tz;
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MoveMatrix[4, 1] := 0;
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MoveMatrix[4, 2] := 0;
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MoveMatrix[4, 3] := 0;
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MoveMatrix[4, 4] := 1
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end;
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function ResizeMatrix(sx, sy, sz: Real): Matrix;
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begin
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ResizeMatrix[1, 1] := sx;
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ResizeMatrix[1, 2] := 0;
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ResizeMatrix[1, 3] := 0;
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ResizeMatrix[1, 4] := 0;
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ResizeMatrix[2, 1] := 0;
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ResizeMatrix[2, 2] := sy;
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ResizeMatrix[2, 3] := 0;
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ResizeMatrix[2, 4] := 0;
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ResizeMatrix[3, 1] := 0;
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ResizeMatrix[3, 2] := 0;
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ResizeMatrix[3, 3] := sz;
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ResizeMatrix[3, 4] := 0;
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ResizeMatrix[4, 1] := 0;
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ResizeMatrix[4, 2] := 0;
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ResizeMatrix[4, 3] := 0;
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ResizeMatrix[4, 4] := 1
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end;
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procedure RotateShape(Shape: Object3D);
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var
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rm: Matrix;
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i: Integer;
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c: Column;
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begin
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rm := RotateMatrix(Shape.xa, Shape.ya, Shape.za); { сгенерировать матрицу вращения }
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c[4] := 1; { последний элемент столбца всегда равен единице }
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for i := 0 to High(Shape.vertices) do { цикл по всем вершинам }
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begin { High(a) возвращает верхний индекс массива a }
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c[1] := Shape.vertices[i].x; { инициализация столбца }
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c[2] := Shape.vertices[i].y;
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c[3] := Shape.vertices[i].z;
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c := MCMult(rm, c); { вызов преобразования }
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Shape.vertices[i].x := c[1]; { внесение изменений в модель }
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Shape.vertices[i].y := c[2]; { в соответствии с полученным }
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Shape.vertices[i].z := c[3] { результатом преобразования }
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end
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end;
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procedure MoveShape(Shape: Object3D; Width, Height: Real);
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begin
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if Shape.xc > Width then
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begin
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Shape.xc := Width;
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Shape.Vx := -Shape.Vx
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end;
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if Shape.xc < -Width then
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begin
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Shape.xc := -Width;
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Shape.Vx := -Shape.Vx
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end;
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if Shape.yc > Height then
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begin
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Shape.yc := Height;
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Shape.Vy := -Shape.Vy
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end;
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if Shape.yc < -Height then
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begin
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Shape.yc := -Height;
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Shape.Vy := -Shape.Vy
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end;
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if Shape.zc > 500 then
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begin
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Shape.zc := 500;
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Shape.Vz := -Shape.Vz
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end;
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if Shape.zc < 200 then
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begin
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Shape.zc := 200;
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Shape.Vz := -Shape.Vz
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end;
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end;
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procedure ResizeShape(var Shape: Object3D; sx, sy, sz: Real);
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var
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mm: Matrix;
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i: Integer;
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c: Column;
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begin
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mm := ResizeMatrix(sx, sy, sz);
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c[4] := 1;
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for i := 0 to High(Shape.vertices) do
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begin
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c[1] := Shape.vertices[i].x;
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c[2] := Shape.vertices[i].y;
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c[3] := Shape.vertices[i].z;
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c := MCMult(mm, c);
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Shape.vertices[i].x := c[1];
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Shape.vertices[i].y := c[2];
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Shape.vertices[i].z := c[3]
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end
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end;
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end.
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