Добавил третью главу занимательного программирования

1 files changed, 302 insertions, 0 deletions

diff --git a/Занимательное программирование/3/2_projection/geometry.pas b/Занимательное программирование/3/2_projection/geometry.pas
new file mode 100644
index 0000000..cc00fd7
--- /dev/null
+++ b/Занимательное программирование/3/2_projection/geometry.pas
@@ -0,0 +1,302 @@
+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 = record

+    vertices: array of Vertex; { вершины }

+    edges: array of Edge; { ребра }

+    xc, yc, zc: Real; { координаты центра объекта }

+  end;

+

+  Matrix = array[1..4, 1..4] of Real; { матрица 4x4 }

+  Column = array[1..4] of Real; { столбец }

+

+function LoadObject3D(filename: String): Object3D;

+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(var Shape: Object3D; xa, ya, za: Real);

+procedure MoveShape(var Shape: Object3D; tx, ty, tz: Real);

+procedure ResizeShape(var Shape: Object3D; sx, sy, sz: Real);

+

+implementation

+

+function LoadObject3D(filename: String): Object3D;

+var

+  F: TextFile; { исходный файл }

+  NV, NE: Integer; { количество вершин, количество ребер }

+  Shape: Object3D; { модель }

+  i: Integer; { счетчик цикла }

+begin

+  AssignFile(F, filename); { открываем  исходный файл }

+  FileMode := 0; { в режиме "только чтение" }

+  Reset(F);

+

+  ReadLn(F, NV); { считываем количество вершин }

+  SetLength(Shape.vertices, NV); { и корректируем размер массива }

+  for i := 0 to NV - 1 do { считываем каждую вершину }

+    ReadLn(F, Shape.vertices[i].x, Shape.vertices[i].y, Shape.vertices[i].z);

+

+  ReadLn(F, NE); { то же для ребер }

+  SetLength(Shape.edges, NE);

+  for i := 0 to NE - 1 do

+    ReadLn(F, Shape.edges[i].src, Shape.edges[i].dest);

+

+  CloseFile(F);

+  LoadObject3D := Shape;

+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(var Shape: Object3D; xa, ya, za: Real);

+var

+  rm: Matrix;

+  i: Integer;

+  c: Column;

+begin

+  rm := RotateMatrix(xa, ya, 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(var Shape: Object3D; tx, ty, tz: Real);

+var

+  mm: Matrix;

+  i: Integer;

+  c: Column;

+begin

+  mm := MoveMatrix(tx, ty, tz);

+  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;

+

+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.

+