Добавил третью главу занимательного программирования

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2025-12-17 12:12:16 +01:00
parent 2878f1e34c
commit 6d7c43c85f
34 changed files with 4191 additions and 0 deletions

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@@ -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.