diff options
Diffstat (limited to 'Занимательное программирование/3/5_ideal_gas/geometry.pas')
| -rw-r--r-- | Занимательное программирование/3/5_ideal_gas/geometry.pas | 344 |
1 files changed, 344 insertions, 0 deletions
diff --git a/Занимательное программирование/3/5_ideal_gas/geometry.pas b/Занимательное программирование/3/5_ideal_gas/geometry.pas new file mode 100644 index 0000000..cbbff5d --- /dev/null +++ b/Занимательное программирование/3/5_ideal_gas/geometry.pas @@ -0,0 +1,344 @@ +unit Geometry;
+
+{$mode ObjFPC}{$H+}
+
+interface
+
+uses
+ Classes, SysUtils;
+
+type
+ { Вершины }
+ Vertex = record
+ x, y, z: Real; { Координаты вершины }
+ end;
+ { Ребра }
+ Edge = record
+ src, dest: Integer; { Индексы соединяемых вершин }
+ end;
+
+ Object3D = class
+ public
+ vertices: array of Vertex; { вершины }
+ edges: array of Edge; { ребра }
+ xc, yc, zc: Real; { координаты центра объекта }
+ vx, vy, vz: Real; { значения составляющих его скорости }
+ xa, ya, za: Real; { скорость вращения вокруг оси }
+
+ constructor Create(var center, velocity, axis: Vertex);
+
+ procedure MoveCenter();
+ end;
+
+ Matrix = array[1..4, 1..4] of Real; { матрица 4x4 }
+ Column = array[1..4] of Real; { столбец }
+
+function CopyObject3D(Shape: Object3D): Object3D;
+
+{ умножение матрицы на матрицу }
+function MMMult(lhs, rhs: Matrix): Matrix;
+{ умножение матрицы на столбец }
+function MCMult(lhs: Matrix; rhs: Column): Column;
+{ матрица поворота модели }
+function RotateMatrix(xa, ya, za: Real): Matrix;
+function MoveMatrix(tx, ty, tz: Real): Matrix;
+function ResizeMatrix(sx, sy, sz: Real): Matrix;
+procedure RotateShape(Shape: Object3D);
+procedure MoveShape(Shape: Object3D; Width, Height: Real);
+procedure ResizeShape(var Shape: Object3D; sx, sy, sz: Real);
+
+implementation
+
+constructor Object3D.Create(var center, velocity, axis: Vertex);
+const
+ size = 10;
+ cubeVertices: array of Vertex = (
+ (x: -size; y: -size; z: -size),
+ (x: -size; y: size; z: -size),
+ (x: size; y: size; z: -size),
+ (x: size; y: -size; z: -size),
+ (x: -size; y: -size; z: size),
+ (x: -size; y: size; z: size),
+ (x: size; y: size; z: size),
+ (x: size; y: -size; z: size)
+ );
+ cubeEdges: array of Edge = (
+ (src: 0; dest: 1),
+ (src: 1; dest: 2),
+ (src: 2; dest: 3),
+ (src: 3; dest: 0),
+ (src: 4; dest: 5),
+ (src: 5; dest: 6),
+ (src: 6; dest: 7),
+ (src: 7; dest: 4),
+ (src: 0; dest: 4),
+ (src: 1; dest: 5),
+ (src: 2; dest: 6),
+ (src: 3; dest: 7)
+ );
+begin
+ vertices := cubeVertices;
+ edges := cubeEdges;
+ xc := center.x;
+ yc := center.y;
+ zc := center.z;
+ vx := velocity.x;
+ vy := velocity.y;
+ vz := velocity.z;
+ xa := axis.x;
+ ya := axis.y;
+ za := axis.z
+end;
+
+procedure Object3D.MoveCenter();
+begin
+ xc := xc + Vx;
+ yc := yc + Vy;
+ zc := zc + Vz
+end;
+
+function CopyObject3D(Shape: Object3D): Object3D;
+begin
+ CopyObject3D.vertices := Copy(Shape.vertices, 0);
+ CopyObject3D.edges := Copy(Shape.edges, 0);
+
+ CopyObject3D.xc := Shape.xc;
+ CopyObject3D.yc := Shape.yc;
+ CopyObject3D.zc := Shape.zc
+end;
+
+function MMMult(lhs, rhs: Matrix): Matrix;
+var
+ i, j, k: Integer;
+ r: Matrix;
+ s: Real;
+begin
+ for i := 1 to 4 do
+ for j := 1 to 4 do
+ begin
+ s := 0;
+ for k := 1 to 4 do
+ s := s + lhs[i, k] * rhs[k, j];
+ r[i, j] := s;
+ end;
+ MMMult := r;
+end;
+
+function MCMult(lhs: Matrix; rhs: Column): Column;
+var
+ k, i: Integer;
+ s: Real;
+ r: Column;
+begin
+ for i := 1 to 4 do { аналогично MMMult }
+ begin
+ s := 0;
+
+ for k := 1 to 4 do
+ s := s + lhs[i, k] * rhs[k];
+ r[i] := s;
+ end;
+
+ MCMult := r;
+end;
+
+function RotateMatrix(xa, ya, za: Real): Matrix;
+var
+ xr, yr, zr: Matrix;
+begin
+ { матрица поворота вокруг оси Ox }
+ xr[1, 1] := 1;
+ xr[1, 2] := 0;
+ xr[1, 3] := 0;
+ xr[1, 4] := 0;
+
+ xr[2, 1] := 0;
+ xr[2, 2] := Cos(xa);
+ xr[2, 3] := -Sin(xa);
+ xr[2, 4] := 0;
+
+ xr[3, 1] := 0;
+ xr[3, 2] := Sin(xa);
+ xr[3, 3] := Cos(xa);
+ xr[3, 4] := 0;
+
+ xr[4, 1] := 0;
+ xr[4, 2] := 0;
+ xr[4, 3] := 0;
+ xr[4, 4] := 1;
+
+ { матрица поворота вокруг оси Oy }
+ yr[1, 1] := Cos(ya);
+ yr[1, 2] := 0;
+ yr[1, 3] := Sin(ya);
+ yr[1, 4] := 0;
+
+ yr[2, 1] := 0;
+ yr[2, 2] := 1;
+ yr[2, 3] := 0;
+ yr[2, 4] := 0;
+
+ yr[3, 1] := -Sin(ya);
+ yr[3, 2] := 0;
+ yr[3, 3] := Cos(ya);
+ yr[3, 4] := 0;
+
+ yr[4, 1] := 0;
+ yr[4, 2] := 0;
+ yr[4, 3] := 0;
+ yr[4, 4] := 1;
+
+ { матрица поворота вокруг оси Oz }
+ zr[1, 1] := Cos(za);
+ zr[1, 2] := -Sin(za);
+ zr[1, 3] := 0;
+ zr[1, 4] := 0;
+
+ zr[2, 1] := Sin(za);
+ zr[2, 2] := Cos(za);
+ zr[2, 3] := 0;
+ zr[2, 4] := 0;
+
+ zr[3, 1] := 0;
+ zr[3, 2] := 0;
+ zr[3, 3] := 1;
+ zr[3, 4] := 0;
+
+ zr[4, 1] := 0;
+ zr[4, 2] := 0;
+ zr[4, 3] := 0;
+ zr[4, 4] := 1;
+
+ RotateMatrix := MMMult(MMMult(xr, yr), zr)
+end;
+
+function MoveMatrix(tx, ty, tz: Real): Matrix;
+begin
+ MoveMatrix[1, 1] := 1;
+ MoveMatrix[1, 2] := 0;
+ MoveMatrix[1, 3] := 0;
+ MoveMatrix[1, 4] := tx;
+
+ MoveMatrix[2, 1] := 0;
+ MoveMatrix[2, 2] := 1;
+ MoveMatrix[2, 3] := 0;
+ MoveMatrix[2, 4] := ty;
+
+ MoveMatrix[3, 1] := 0;
+ MoveMatrix[3, 2] := 0;
+ MoveMatrix[3, 3] := 1;
+ MoveMatrix[3, 4] := tz;
+
+ MoveMatrix[4, 1] := 0;
+ MoveMatrix[4, 2] := 0;
+ MoveMatrix[4, 3] := 0;
+ MoveMatrix[4, 4] := 1
+end;
+
+function ResizeMatrix(sx, sy, sz: Real): Matrix;
+begin
+ ResizeMatrix[1, 1] := sx;
+ ResizeMatrix[1, 2] := 0;
+ ResizeMatrix[1, 3] := 0;
+ ResizeMatrix[1, 4] := 0;
+
+ ResizeMatrix[2, 1] := 0;
+ ResizeMatrix[2, 2] := sy;
+ ResizeMatrix[2, 3] := 0;
+ ResizeMatrix[2, 4] := 0;
+
+ ResizeMatrix[3, 1] := 0;
+ ResizeMatrix[3, 2] := 0;
+ ResizeMatrix[3, 3] := sz;
+ ResizeMatrix[3, 4] := 0;
+
+ ResizeMatrix[4, 1] := 0;
+ ResizeMatrix[4, 2] := 0;
+ ResizeMatrix[4, 3] := 0;
+ ResizeMatrix[4, 4] := 1
+end;
+
+procedure RotateShape(Shape: Object3D);
+var
+ rm: Matrix;
+ i: Integer;
+ c: Column;
+begin
+ rm := RotateMatrix(Shape.xa, Shape.ya, Shape.za); { сгенерировать матрицу вращения }
+ c[4] := 1; { последний элемент столбца всегда равен единице }
+
+ for i := 0 to High(Shape.vertices) do { цикл по всем вершинам }
+ begin { High(a) возвращает верхний индекс массива a }
+ c[1] := Shape.vertices[i].x; { инициализация столбца }
+ c[2] := Shape.vertices[i].y;
+ c[3] := Shape.vertices[i].z;
+
+ c := MCMult(rm, c); { вызов преобразования }
+
+ Shape.vertices[i].x := c[1]; { внесение изменений в модель }
+ Shape.vertices[i].y := c[2]; { в соответствии с полученным }
+ Shape.vertices[i].z := c[3] { результатом преобразования }
+ end
+end;
+
+procedure MoveShape(Shape: Object3D; Width, Height: Real);
+begin
+ if Shape.xc > Width then
+ begin
+ Shape.xc := Width;
+ Shape.Vx := -Shape.Vx
+ end;
+ if Shape.xc < -Width then
+ begin
+ Shape.xc := -Width;
+ Shape.Vx := -Shape.Vx
+ end;
+
+ if Shape.yc > Height then
+ begin
+ Shape.yc := Height;
+ Shape.Vy := -Shape.Vy
+ end;
+ if Shape.yc < -Height then
+ begin
+ Shape.yc := -Height;
+ Shape.Vy := -Shape.Vy
+ end;
+
+ if Shape.zc > 500 then
+ begin
+ Shape.zc := 500;
+ Shape.Vz := -Shape.Vz
+ end;
+ if Shape.zc < 200 then
+ begin
+ Shape.zc := 200;
+ Shape.Vz := -Shape.Vz
+ end;
+end;
+
+procedure ResizeShape(var Shape: Object3D; sx, sy, sz: Real);
+var
+ mm: Matrix;
+ i: Integer;
+ c: Column;
+begin
+ mm := ResizeMatrix(sx, sy, sz);
+ c[4] := 1;
+
+ for i := 0 to High(Shape.vertices) do
+ begin
+ c[1] := Shape.vertices[i].x;
+ c[2] := Shape.vertices[i].y;
+ c[3] := Shape.vertices[i].z;
+
+ c := MCMult(mm, c);
+
+ Shape.vertices[i].x := c[1];
+ Shape.vertices[i].y := c[2];
+ Shape.vertices[i].z := c[3]
+ end
+end;
+
+end.
+
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