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Zhe Yuan
2026-03-31 10:26:51 -04:00
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commit 126d308543
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15
lab3/Lab3 grids/cylinder-A.grid2D Normal file
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GRID2D_OF_POINTS3D
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30
lab3/Lab3 grids/sphere-A.grid2D Normal file
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GRID2D_OF_POINTS3D
# Dimensions
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43
lab3/Lab3 grids/sphere-A.off Normal file
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38
lab3/Lab3 grids/torus-A.grid2D Normal file
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GRID2D_OF_POINTS3D
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65
lab3/Lab3 grids/torus-A.off Normal file
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57
lab3/Lab3 grids/wave-A.off Normal file
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17
lab3/Lab3 simple grids/grid2D-2x3-A-subdiv-1.grid2D Normal file
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GRID2D_OF_POINTS3D
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58
lab3/Lab3 simple grids/grid2D-2x3-A-subdiv-1.off Normal file
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47
lab3/Lab3 simple grids/grid2D-2x3-A-subdiv-2.grid2D Normal file
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GRID2D_OF_POINTS3D
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1.5 0.5 1.5
1.75 0.5 1.5
2.0 0.5 1.5
0.0 0.25 1.75
0.25 0.25 1.75
0.5 0.25 1.75
0.75 0.25 1.75
1.0 0.25 1.75
1.25 0.25 1.75
1.5 0.25 1.75
1.75 0.25 1.75
2.0 0.25 1.75
0.0 0.0 2.0
0.25 0.0 2.0
0.5 0.0 2.0
0.75 0.0 2.0
1.0 0.0 2.0
1.25 0.0 2.0
1.5 0.0 2.0
1.75 0.0 2.0
2.0 0.0 2.0

180
lab3/Lab3 simple grids/plane-2x2-A-subdiv-3.off Normal file
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@@ -0,0 +1,180 @@
OFF
# G
# r
# i
# d
#
# s
# u
# b
# d
# i
# v
# i
# d
# e
# d
#
# i
# n
#
# 3
#
# i
# t
# e
# r
# a
# t
# i
# o
# n
# s
# .
81 64 0
0.0 2.0 0.0
0.25 2.0 0.0
0.5 2.0 0.0
0.75 2.0 0.0
1.0 2.0 0.0
1.25 2.0 0.0
1.5 2.0 0.0
1.75 2.0 0.0
2.0 2.0 0.0
0.0 1.75 0.25
0.25 1.75 0.25
0.5 1.75 0.25
0.75 1.75 0.25
1.0 1.75 0.25
1.25 1.75 0.25
1.5 1.75 0.25
1.75 1.75 0.25
2.0 1.75 0.25
0.0 1.5 0.5
0.25 1.5 0.5
0.5 1.5 0.5
0.75 1.5 0.5
1.0 1.5 0.5
1.25 1.5 0.5
1.5 1.5 0.5
1.75 1.5 0.5
2.0 1.5 0.5
0.0 1.25 0.75
0.25 1.25 0.75
0.5 1.25 0.75
0.75 1.25 0.75
1.0 1.25 0.75
1.25 1.25 0.75
1.5 1.25 0.75
1.75 1.25 0.75
2.0 1.25 0.75
0.0 1.0 1.0
0.25 1.0 1.0
0.5 1.0 1.0
0.75 1.0 1.0
1.0 1.0 1.0
1.25 1.0 1.0
1.5 1.0 1.0
1.75 1.0 1.0
2.0 1.0 1.0
0.0 0.75 1.25
0.25 0.75 1.25
0.5 0.75 1.25
0.75 0.75 1.25
1.0 0.75 1.25
1.25 0.75 1.25
1.5 0.75 1.25
1.75 0.75 1.25
2.0 0.75 1.25
0.0 0.5 1.5
0.25 0.5 1.5
0.5 0.5 1.5
0.75 0.5 1.5
1.0 0.5 1.5
1.25 0.5 1.5
1.5 0.5 1.5
1.75 0.5 1.5
2.0 0.5 1.5
0.0 0.25 1.75
0.25 0.25 1.75
0.5 0.25 1.75
0.75 0.25 1.75
1.0 0.25 1.75
1.25 0.25 1.75
1.5 0.25 1.75
1.75 0.25 1.75
2.0 0.25 1.75
0.0 0.0 2.0
0.25 0.0 2.0
0.5 0.0 2.0
0.75 0.0 2.0
1.0 0.0 2.0
1.25 0.0 2.0
1.5 0.0 2.0
1.75 0.0 2.0
2.0 0.0 2.0
4 0 1 10 9
4 1 2 11 10
4 2 3 12 11
4 3 4 13 12
4 4 5 14 13
4 5 6 15 14
4 6 7 16 15
4 7 8 17 16
4 9 10 19 18
4 10 11 20 19
4 11 12 21 20
4 12 13 22 21
4 13 14 23 22
4 14 15 24 23
4 15 16 25 24
4 16 17 26 25
4 18 19 28 27
4 19 20 29 28
4 20 21 30 29
4 21 22 31 30
4 22 23 32 31
4 23 24 33 32
4 24 25 34 33
4 25 26 35 34
4 27 28 37 36
4 28 29 38 37
4 29 30 39 38
4 30 31 40 39
4 31 32 41 40
4 32 33 42 41
4 33 34 43 42
4 34 35 44 43
4 36 37 46 45
4 37 38 47 46
4 38 39 48 47
4 39 40 49 48
4 40 41 50 49
4 41 42 51 50
4 42 43 52 51
4 43 44 53 52
4 45 46 55 54
4 46 47 56 55
4 47 48 57 56
4 48 49 58 57
4 49 50 59 58
4 50 51 60 59
4 51 52 61 60
4 52 53 62 61
4 54 55 64 63
4 55 56 65 64
4 56 57 66 65
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4 58 59 68 67
4 59 60 69 68
4 60 61 70 69
4 61 62 71 70
4 63 64 73 72
4 64 65 74 73
4 65 66 75 74
4 66 67 76 75
4 67 68 77 76
4 68 69 78 77
4 69 70 79 78
4 70 71 80 79

8
lab3/Lab3 simple grids/plane-2x2-A.grid2D Normal file
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GRID2D_OF_POINTS3D
# Dimensions
2 2
0 2 0
2 2 0
0 0 2
2 0 2

9
lab3/Lab3 simple grids/plane-2x2-A.off Normal file
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@@ -0,0 +1,9 @@
OFF
# File created from 2D grid of points.
4 1 0
0.0 2.0 0.0
2.0 2.0 0.0
0.0 0.0 2.0
2.0 0.0 2.0
4 0 1 3 2

29
lab3/Makefile Normal file
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CXX = g++
CXXFLAGS = -Wall -O2
TARGETS = print_grid2D grid2off test_grid2DIO subdivide_grid
all: $(TARGETS)
print_grid2D: print_grid2D.cpp grid2DIO.o
$(CXX) $(CXXFLAGS) -o $@ $^
grid2off: grid2off.cpp grid2DIO.o writeGrid2DOFF.o
$(CXX) $(CXXFLAGS) -o $@ $^
test_grid2DIO: test_grid2DIO.cpp grid2DIO.o
$(CXX) $(CXXFLAGS) -o $@ $^
subdivide_grid: subdivide_grid.cpp grid2DIO.o writeGrid2DOFF.o
$(CXX) $(CXXFLAGS) -o $@ $^
grid2DIO.o: grid2DIO.cpp grid2DIO.h grid2DPoints3D.h
$(CXX) $(CXXFLAGS) -c -o $@ $<
writeGrid2DOFF.o: writeGrid2DOFF.cpp writeGrid2DOFF.h grid2DPoints3D.h
$(CXX) $(CXXFLAGS) -c -o $@ $<
clean:
rm -f *.o $(TARGETS)
.PHONY: all clean

73
lab3/README.md Normal file
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# Lab 3: Stencil-Based Grid Subdivision
## How to Build
### Windows
Use Visual Studio (Developer Command Prompt) to compile the code.
```bat
.\make.bat
```
> **Note:** `cl` is only available in the Developer Command Prompt, change the path of `VsDevCmd.bat` in `make.bat` first.
### Linux / macOS — GCC via Makefile
```
make
```
This compiles all targets including `subdivide_grid`.
## How to Run
### Windows
```bat
subdivide_grid.exe {num_iter} {input_file}
```
### Linux / macOS
```bash
./subdivide_grid {num_iter} {input_file}
```
- `{num_iter}`: integer number of subdivision iterations (>= 0)
- `{input_file}`: a `.grid2D` file
The output file is written to the same directory as the input, with the suffix
`-subdiv.grid2D` appended (replacing the `.grid2D` extension).
### Optional `-off` flag
```bash
./subdivide_grid -off {num_iter} {input_file}
```
With `-off`, the program additionally writes a Geomview `.off` file named
`{basename}-subdiv.off`.
### Examples
```bash
./subdivide_grid 1 "Lab3 simple grids/grid2D-2x3-A.grid2D"
./subdivide_grid 3 "Lab3 grids/wave-A.grid2D"
./subdivide_grid -off 3 "Lab3 grids/sphere-A.grid2D"
```
## Visualization
Convert a `.grid2D` file to Geomview `.off` format:
```bash
./grid2off {input.grid2D}
```
## AI Tools Used
**GitHub Copilot** (via VS Code) was used for:
- Auto generating `Makefile` and this `README.md`.

224
lab3/grid2DIO.cpp Normal file
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// Functions to read/write a 2D grid of 3D points.
#include "grid2DIO.h"
#include <fstream>
#include <iostream>
#include <sstream>
#include <stdexcept>
#include <string>
const std::string GRID2D_POINTS3D_HEADER = "GRID2D_OF_POINTS3D";
// ********************************************************************************
// Internal helpers
// ********************************************************************************
/// Trim leading and trailing whitespace from s.
static std::string Trim(const std::string& s) {
const std::string whitespace = " \t\r\n";
size_t start = s.find_first_not_of(whitespace);
if (start == std::string::npos) { return ""; }
size_t end = s.find_last_not_of(whitespace);
return s.substr(start, end - start + 1);
}
/// Throw a read error with two descriptive lines.
static void RaiseReadErrorII(int iline,
const std::string& error_line1,
const std::string& error_line2)
{
throw std::runtime_error(
"Error reading line " + std::to_string(iline) + ": " +
error_line1 + "\n " + error_line2);
}
// ********************************************************************************
// Read/Write helper predicates
// ********************************************************************************
bool IsHeader(const std::string& line) {
return Trim(line) == GRID2D_POINTS3D_HEADER;
}
bool IsCommentOrBlankLine(const std::string& line) {
std::string s = Trim(line);
if (s.empty()) { return true; }
if (s[0] == '#') { return true; }
return false;
}
// ********************************************************************************
// Read functions
// ********************************************************************************
void ReadGrid2DPoints3D(std::istream& infile, GRID2D_POINTS3D& grid2D) {
// Read coordinates of point [i,j] in grid.
int i = 0, j = 0, iline = 1;
std::string line;
while (std::getline(infile, line)) {
std::string trimmed = Trim(line);
if (iline == 1) {
if (!IsHeader(trimmed)) {
RaiseReadErrorII(1,
"Incorrect file header.",
"Expected header: " + GRID2D_POINTS3D_HEADER);
}
}
else if (!IsCommentOrBlankLine(trimmed)) {
if (!grid2D.AreDimensionsSet()) {
std::istringstream iss(trimmed);
int n, m;
if (!(iss >> n >> m)) {
RaiseReadErrorII(iline,
"Incorrect grid dimensions.",
"Expecting two integers for grid dimensions.");
}
std::string extra;
if (iss >> extra) {
RaiseReadErrorII(iline,
"Incorrect grid dimensions.",
"Expecting two integers for grid dimensions.");
}
grid2D.SetDimensions(n, m);
}
else {
std::istringstream iss(trimmed);
double x, y, z;
if (!(iss >> x >> y >> z)) {
RaiseReadErrorII(iline,
"Error reading point coordinates.",
"Expecting three float coordinates for each point.");
}
if (i >= grid2D.NumRows()) {
std::cerr << "Warning: More than "
<< grid2D.NumRows() << " x "
<< grid2D.NumCols()
<< " points in file.\n";
std::cerr << "Skipping remaining points after line "
<< iline << ".\n";
break;
}
grid2D.SetCoord(i, j, x, y, z);
j++;
if (j >= grid2D.NumCols()) {
j = 0;
i++;
}
}
}
iline++;
}
if (i < grid2D.NumRows()) {
throw std::runtime_error(
"Too few points in file. Expected coordinates of " +
std::to_string(grid2D.NumPoints()) + " points.\n" +
" Found coordinates of " +
std::to_string(i * grid2D.NumCols() + j) + " points.\n" +
" First missing point: [" +
std::to_string(i) + "," + std::to_string(j) + "].");
}
}
void OpenReadGrid2DPoints3D(const std::string& filename,
GRID2D_POINTS3D& grid2D)
{
try {
std::ifstream infile(filename);
if (!infile.is_open()) {
std::cerr << "Input file " << filename << " not found.\n";
throw std::runtime_error(
"Input file " + filename + " not found.");
}
ReadGrid2DPoints3D(infile, grid2D);
}
catch (const std::out_of_range& e) {
std::cerr << "Error reading file " << filename
<< ".\n " << e.what() << "\n";
throw;
}
catch (const std::runtime_error& e) {
std::cerr << "Error reading file " << filename
<< ".\n " << e.what() << "\n";
throw;
}
catch (const std::exception& e) {
std::cerr << "Error reading file " << filename
<< ".\n " << e.what() << "\n";
throw;
}
}
// ********************************************************************************
// Write functions
// ********************************************************************************
void WriteGrid2DPoints3D(std::ostream& outfile,
const GRID2D_POINTS3D& grid2D,
const std::vector<std::string>& comment_list)
{
// Write header
outfile << GRID2D_POINTS3D_HEADER << "\n";
// Write dimensions
outfile << grid2D.NumRows() << " " << grid2D.NumCols() << "\n";
// Write comments
for (const auto& comment : comment_list) {
outfile << "# " << comment << "\n";
}
// Write point coordinates
for (int irow = 0; irow < grid2D.NumRows(); irow++) {
for (int icol = 0; icol < grid2D.NumCols(); icol++) {
auto c = grid2D.Coord(irow, icol);
outfile << c[0] << " " << c[1] << " " << c[2] << "\n";
}
}
}
void OpenWriteGrid2DPoints3D(const std::string& filename,
const GRID2D_POINTS3D& grid2D,
const std::vector<std::string>& comment_list)
{
try {
std::ofstream outfile(filename);
if (!outfile.is_open()) {
std::cerr << "Cannot open file " << filename
<< " for writing.\n";
throw std::runtime_error(
"Cannot open file " + filename + " for writing.");
}
WriteGrid2DPoints3D(outfile, grid2D, comment_list);
}
catch (const std::out_of_range& e) {
std::cerr << "Error writing file " << filename
<< ".\n " << e.what() << "\n";
throw;
}
catch (const std::runtime_error& e) {
std::cerr << "Error writing file " << filename
<< ".\n " << e.what() << "\n";
throw;
}
catch (const std::exception& e) {
std::cerr << "Error writing file " << filename
<< ".\n " << e.what() << "\n";
throw;
}
}

38
lab3/grid2DIO.h Normal file
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// Functions to read/write a 2D grid of 3D points.
#ifndef GRID2DIO_H
#define GRID2DIO_H
#include <iostream>
#include <string>
#include <vector>
#include "grid2DPoints3D.h"
// Header string used in grid2D files.
extern const std::string GRID2D_POINTS3D_HEADER;
/// Return true if line equals the grid2D file header.
bool IsHeader(const std::string& line);
/// Return true if line is a comment line (starts with '#') or blank.
bool IsCommentOrBlankLine(const std::string& line);
/// Read grid2D from an open input stream.
void ReadGrid2DPoints3D(std::istream& infile, GRID2D_POINTS3D& grid2D);
/// Open filename and read grid2D from it.
void OpenReadGrid2DPoints3D(const std::string& filename,
GRID2D_POINTS3D& grid2D);
/// Write grid2D to an open output stream.
void WriteGrid2DPoints3D(std::ostream& outfile,
const GRID2D_POINTS3D& grid2D,
const std::vector<std::string>& comment_list = {});
/// Open filename and write grid2D to it.
void OpenWriteGrid2DPoints3D(const std::string& filename,
const GRID2D_POINTS3D& grid2D,
const std::vector<std::string>& comment_list = {});
#endif // GRID2DIO_H

136
lab3/grid2DPoints3D.h Normal file
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// Class representing 2D grid of points in 3D.
#ifndef GRID2D_POINTS3D_H
#define GRID2D_POINTS3D_H
#include <array>
#include <iostream>
#include <stdexcept>
#include <string>
#include <vector>
// ********************************************************************************
// Class GRID2D_POINTS3D
// ********************************************************************************
/// A class to store a 2D grid of 3D points.
class GRID2D_POINTS3D {
public:
static const int DIM3 = 3;
int num_rows;
int num_cols;
/// coord[i][j] = {x, y, z} for grid point at row i, column j.
std::vector<std::vector<std::array<double, 3>>> coord;
bool are_dimensions_set;
GRID2D_POINTS3D() :
num_rows(0), num_cols(0), are_dimensions_set(false) {}
void SetDimensions(int n, int m) {
num_rows = n;
num_cols = m;
coord.assign(n, std::vector<std::array<double, 3>>(
m, {0.0, 0.0, 0.0}));
are_dimensions_set = true;
}
bool AreDimensionsSet() const {
return are_dimensions_set;
}
int NumRows() const { return num_rows; }
int NumCols() const { return num_cols; }
int NumPoints() const { return num_rows * num_cols; }
int NumQuadrilaterals() const {
if (num_rows < 2 || num_cols < 2) { return 0; }
return (num_rows - 1) * (num_cols - 1);
}
int PointDimension() const { return DIM3; }
/// Index of point (irow, icol) in a flat array.
/// k'th point in array coord has index (k-1).
int PointIndex(int irow, int icol) const {
return irow * NumCols() + icol;
}
/// Return false and error message if (index < 0) or (index >= iupper).
std::pair<bool, std::string> CheckIndex(
int index, int iupper,
const std::string& index_name) const
{
if (index < 0) {
return {false,
"Illegal negative " + index_name + " index " +
std::to_string(index) + "."};
}
if (index >= iupper) {
std::string name = index_name;
name[0] = static_cast<char>(toupper(
static_cast<unsigned char>(name[0])));
return {false,
name + " " + std::to_string(index) +
" is out of bounds.\n" +
" " + name + " index should be less than " +
std::to_string(iupper) + "."};
}
return {true, ""};
}
/// Raise std::out_of_range if (index < 0) or (index >= iupper).
void CheckIndexRaiseError(
int index, int iupper,
const std::string& index_name,
const std::string& function_name) const
{
auto result = CheckIndex(index, iupper, index_name);
if (!result.first) {
throw std::out_of_range(
"Error in GRID2D_POINTS3D::" + function_name +
". " + result.second);
}
}
/// Return coordinates of grid point [irow][jcol].
/// Precondition: [irow][jcol] are in appropriate bounds.
std::array<double, 3> Coord(int irow, int jcol) const {
return coord[irow][jcol];
}
/// Set coord[irow][jcol] to (x, y, z).
void SetCoord(int irow, int jcol, double x, double y, double z) {
CheckIndexRaiseError(irow, NumRows(), "Row", "SetCoord");
CheckIndexRaiseError(jcol, NumCols(), "Column", "SetCoord");
coord[irow][jcol] = {x, y, z};
}
/// Print grid in formatted mode. Mainly for debugging.
void FormattedPrint() const {
std::cout << "Grid dimensions: " << num_rows << " x "
<< num_cols << "\n";
std::cout << "Point Coordinates:\n";
for (int i = 0; i < num_rows; i++) {
for (int j = 0; j < num_cols; j++) {
std::cout << " [" << i << "][" << j << "]: "
<< coord[i][j][0] << " "
<< coord[i][j][1] << " "
<< coord[i][j][2] << "\n";
}
}
}
};
#endif // GRID2D_POINTS3D_H

76
lab3/grid2off.cpp Normal file
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// Convert 2D grid of points to Geomview .off file of quadrilaterals.
#include <iostream>
#include <string>
#include "grid2DPoints3D.h"
#include "grid2DIO.h"
#include "writeGrid2DOFF.h"
// ********************* Functions ************************************
/// Replace the file extension of infilename with ".off".
std::string CreateOutFilename(const std::string& infilename) {
size_t dot_pos = infilename.rfind('.');
std::string basename;
if (dot_pos != std::string::npos) {
basename = infilename.substr(0, dot_pos);
}
else {
basename = infilename;
}
return basename + ".off";
}
void UsageMsg(const std::string& command_name) {
std::cerr << "Usage: " << command_name
<< " {input filename} [{output filename}]\n";
}
// ********************* Main *****************************************
int main(int argc, char* argv[]) {
if (argc == 1) {
UsageMsg(argv[0]);
return 0;
}
std::string infilename = argv[1];
GRID2D_POINTS3D grid2D;
try {
OpenReadGrid2DPoints3D(infilename, grid2D);
}
catch (const std::exception&) {
std::cerr << "Exiting...\n";
return -1;
}
std::string outfilename;
if (argc < 3) {
outfilename = CreateOutFilename(infilename);
}
else {
outfilename = argv[2];
}
WRITE_GRID2D_OFF writeOFF;
std::vector<std::string> comments_list =
{"File created from 2D grid of points."};
try {
std::cout << "Writing file " << outfilename << ".\n";
writeOFF.OpenAndWrite(outfilename, grid2D, comments_list);
}
catch (const std::exception& e) {
std::cerr << e.what() << "\n";
std::cerr << "Exiting...\n";
return -1;
}
return 0;
}

38
lab3/make.bat Normal file
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@echo off
setlocal
set "CALLER_DIR=%cd%"
set "SCRIPT_DIR=%~dp0"
set "VSDEVCMD=C:\Program Files\Microsoft Visual Studio\2022\Community\Common7\Tools\VsDevCmd.bat"
if /I "%~1"=="clean" goto clean
if not exist "%VSDEVCMD%" (
echo VsDevCmd.bat not found:
echo %VSDEVCMD%
exit /b 1
)
call "%VSDEVCMD%"
if errorlevel 1 exit /b 1
cd /d "%SCRIPT_DIR%"
cl /EHsc /W3 /O2 /Fe:subdivide_grid.exe subdivide_grid.cpp grid2DIO.cpp writeGrid2DOFF.cpp
cl /EHsc /W3 /O2 /Fe:grid2off.exe grid2off.cpp grid2DIO.cpp writeGrid2DOFF.cpp
cl /EHsc /W3 /O2 /Fe:print_grid2D.exe print_grid2D.cpp grid2DIO.cpp
cl /EHsc /W3 /O2 /Fe:test_grid2DIO.exe test_grid2DIO.cpp grid2DIO.cpp
cd /d "%CALLER_DIR%"
endlocal
exit /b 0
:clean
cd /d "%SCRIPT_DIR%"
del /q subdivide_grid.exe subdivide_grid.obj grid2DIO.obj writeGrid2DOFF.obj subdivide_grid.pdb vc140.pdb vc140.idb subdivide_grid.ilk 2>nul
del /q grid2off.exe grid2off.obj 2>nul
del /q print_grid2D.exe print_grid2D.obj 2>nul
del /q test_grid2DIO.exe test_grid2DIO.obj 2>nul
cd /d "%CALLER_DIR%"
endlocal
exit /b 0

40
lab3/print_grid2D.cpp Normal file
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// Read and print a file with format GRID2D_POINTS3D.
// Mainly for testing.
#include <iostream>
#include <string>
#include "grid2DPoints3D.h"
#include "grid2DIO.h"
// ********************* Functions ************************************
void UsageMsg(const std::string& command_name) {
std::cerr << "Usage: " << command_name << " {filename}\n";
}
// ********************* Main *****************************************
int main(int argc, char* argv[]) {
if (argc == 1) {
UsageMsg(argv[0]);
return 0;
}
GRID2D_POINTS3D grid2D;
try {
OpenReadGrid2DPoints3D(argv[1], grid2D);
}
catch (const std::exception&) {
std::cerr << "Exiting...\n";
return -1;
}
grid2D.FormattedPrint();
return 0;
}

256
lab3/subdivide_grid.cpp Normal file
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// Subdivide a 2D grid of 3D points using stencil-based subdivision.
// Usage: subdivide_grid {num_iter} {input_file}
#include <iostream>
#include <string>
#include <vector>
#include <array>
#include "grid2DPoints3D.h"
#include "grid2DIO.h"
#include "writeGrid2DOFF.h"
// helper
// return a * p (scalar multiply).
static std::array<double, 3> Scale(double a, const std::array<double, 3>& p) {
return {a * p[0], a * p[1], a * p[2]};
}
// return p + q (component-wise add).
static std::array<double, 3> Add(const std::array<double, 3>& p,
const std::array<double, 3>& q)
{
return {p[0] + q[0], p[1] + q[1], p[2] + q[2]};
}
// main subdivision function
void SubdivideI_Grid2D(const GRID2D_POINTS3D& grid2D,
GRID2D_POINTS3D& new_grid2D)
{
const int n = grid2D.NumRows();
const int m = grid2D.NumCols();
const int new_n = 2 * n - 1;
const int new_m = 2 * m - 1;
new_grid2D.SetDimensions(new_n, new_m);
auto P = [&](int i, int j) { return grid2D.Coord(i, j); };
auto Set = [&](int I, int J, const std::array<double, 3>& v) {
new_grid2D.SetCoord(I, J, v[0], v[1], v[2]);
};
// (a) Face centers: new vertex (2i+1, 2j+1)
for (int i = 0; i < n - 1; i++) {
for (int j = 0; j < m - 1; j++) {
auto v = Scale(0.25, Add(Add(P(i, j), P(i, j + 1)),
Add(P(i + 1, j), P(i + 1, j + 1))));
Set(2 * i + 1, 2 * j + 1, v);
}
}
// (b) Horizontal edge midpoints: new vertex (2i, 2j+1)
for (int i = 0; i < n; i++) {
for (int j = 0; j < m - 1; j++) {
std::array<double, 3> v;
if (i == 0 || i == n - 1) {
// midpoint of edge endpoints.
v = Scale(0.5, Add(P(i, j), P(i, j + 1)));
}
else {
v = Add(Scale(6.0 / 16.0, Add(P(i, j), P(i, j + 1))),
Scale(1.0 / 16.0, Add(Add(P(i - 1, j), P(i - 1, j + 1)),
Add(P(i + 1, j), P(i + 1, j + 1)))));
}
Set(2 * i, 2 * j + 1, v);
}
}
// (c) Vertical edge midpoints: new vertex (2i+1, 2j)
for (int i = 0; i < n - 1; i++) {
for (int j = 0; j < m; j++) {
std::array<double, 3> v;
if (j == 0 || j == m - 1) {
// midpoint of edge endpoints.
v = Scale(0.5, Add(P(i, j), P(i + 1, j)));
}
else {
v = Add(Scale(6.0 / 16.0, Add(P(i, j), P(i + 1, j))),
Scale(1.0 / 16.0, Add(Add(P(i, j - 1), P(i, j + 1)),
Add(P(i + 1, j - 1), P(i + 1, j + 1)))));
}
Set(2 * i + 1, 2 * j, v);
}
}
// (d/e.iii/e.iv/e.v) Original vertices: new vertex (2i, 2j)
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
const bool on_top = (i == 0);
const bool on_bottom = (i == n - 1);
const bool on_left = (j == 0);
const bool on_right = (j == m - 1);
std::array<double, 3> v;
if ((on_top || on_bottom) && (on_left || on_right)) {
// corner (e.iii): copy directly.
v = P(i, j);
}
else if (on_left || on_right) {
// left/right boundary, non-corner (e.iv): (1/8) row-adjacent, (3/4) center.
v = Add(Scale(3.0 / 4.0, P(i, j)),
Scale(1.0 / 8.0, Add(P(i - 1, j), P(i + 1, j))));
}
else if (on_top || on_bottom) {
// top/bottom boundary, non-corner (e.v): (1/8) column-adjacent, (3/4) center.
v = Add(Scale(3.0 / 4.0, P(i, j)),
Scale(1.0 / 8.0, Add(P(i, j - 1), P(i, j + 1))));
}
else {
// interior vertex (d): 9/16 center, 3/32 edge neighbors, 1/64 diagonal neighbors.
v = Scale(9.0 / 16.0, P(i, j));
v = Add(v, Scale(3.0 / 32.0, Add(Add(P(i - 1, j), P(i + 1, j)),
Add(P(i, j - 1), P(i, j + 1)))));
v = Add(v, Scale(1.0 / 64.0, Add(Add(P(i - 1, j - 1), P(i - 1, j + 1)),
Add(P(i + 1, j - 1), P(i + 1, j + 1)))));
}
Set(2 * i, 2 * j, v);
}
}
}
// perform num_iter subdivision by calling SubdivideI_Grid2D repeatedly
// num_iter == 0 -> a copy of grid2D
void SubdivideMulti_Grid2D(const GRID2D_POINTS3D& grid2D,
GRID2D_POINTS3D& result,
int num_iter)
{
if (num_iter == 0) {
result = grid2D;
return;
}
GRID2D_POINTS3D current = grid2D;
GRID2D_POINTS3D next;
for (int iter = 0; iter < num_iter; iter++) {
SubdivideI_Grid2D(current, next);
current = next;
}
result = current;
}
// io
/// construct output name
static std::string CreateOutputFilename(const std::string& infilename) {
const std::string grid2d_ext = ".grid2D";
if (infilename.size() > grid2d_ext.size() &&
infilename.substr(infilename.size() - grid2d_ext.size()) == grid2d_ext)
{
return infilename.substr(0, infilename.size() - grid2d_ext.size())
+ "-subdiv.grid2D";
}
return infilename + "-subdiv.grid2D";
}
static std::string CreateOffOutputFilename(const std::string& infilename) {
const std::string grid2d_ext = ".grid2D";
if (infilename.size() > grid2d_ext.size() &&
infilename.substr(infilename.size() - grid2d_ext.size()) == grid2d_ext)
{
return infilename.substr(0, infilename.size() - grid2d_ext.size())
+ "-subdiv.off";
}
return infilename + "-subdiv.off";
}
void UsageMsg(const std::string& command_name) {
std::cerr << "Usage: " << command_name
<< " [-off] {num_iter} {input_file}\n";
}
// Main
int main(int argc, char* argv[]) {
// Parse optional -off flag.
bool write_off = false;
int arg_start = 1;
if (argc > 1 && std::string(argv[1]) == "-off") {
write_off = true;
arg_start = 2;
}
if (argc - arg_start != 2) {
UsageMsg(argv[0]);
return 0;
}
int num_iter;
try {
num_iter = std::stoi(argv[arg_start]);
}
catch (const std::exception&) {
std::cerr << "Error: num_iter must be an integer.\n";
UsageMsg(argv[0]);
return -1;
}
if (num_iter < 0) {
std::cerr << "Error: num_iter must be non-negative.\n";
return -1;
}
const std::string infilename = argv[arg_start + 1];
GRID2D_POINTS3D grid2D;
try {
OpenReadGrid2DPoints3D(infilename, grid2D);
}
catch (const std::exception&) {
std::cerr << "Exiting...\n";
return -1;
}
GRID2D_POINTS3D result;
SubdivideMulti_Grid2D(grid2D, result, num_iter);
// Write grid2D output.
const std::string outfilename = CreateOutputFilename(infilename);
const std::vector<std::string> comments = {
"Subdivided grid. Iterations: " + std::to_string(num_iter),
"Input: " + infilename
};
try {
std::cout << "Writing " << outfilename << ".\n";
OpenWriteGrid2DPoints3D(outfilename, result, comments);
}
catch (const std::exception&) {
std::cerr << "Exiting...\n";
return -1;
}
// Optionally write .off output.
if (write_off) {
const std::string off_outfilename = CreateOffOutputFilename(infilename);
WRITE_GRID2D_OFF writeOFF;
const std::vector<std::string> off_comments = {
"Subdivided grid in OFF format. Iterations: " + std::to_string(num_iter),
"Input: " + infilename
};
try {
std::cout << "Writing " << off_outfilename << ".\n";
writeOFF.OpenAndWrite(off_outfilename, result, off_comments);
}
catch (const std::exception&) {
std::cerr << "Exiting...\n";
return -1;
}
}
return 0;
}

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// Test read and write functions in grid2DIO.py.
// Mainly for an example of reading and writing a GRID2D_POINTS3D array
#include <iostream>
#include <string>
#include "grid2DPoints3D.h"
#include "grid2DIO.h"
// ********************* Functions ************************************
void UsageMsg(const std::string& command_name) {
std::cerr << "Usage: " << command_name << " {infile} {outfile}\n";
}
// ********************* Main *****************************************
int main(int argc, char* argv[]) {
using namespace std;
if (argc != 3) {
UsageMsg(argv[0]);
return 0;
}
GRID2D_POINTS3D grid2D;
try {
cout << "Reading " << argv[1] << "." << endl;
OpenReadGrid2DPoints3D(argv[1], grid2D);
}
catch (const exception&) {
cerr << "Exiting...\n";
return -1;
}
try {
cout << "Copying to file " << argv[2] << ".";
vector<string> comment_list;
string s = string("Copy of ") + argv[1] + ".";
comment_list.push_back(s);
OpenWriteGrid2DPoints3D(argv[2], grid2D, comment_list);
}
catch (const exception&) {
cerr << "Exiting...\n";
return -1;
}
return 0;
}

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// Functions to write grid2DPoints3D as a Geomview .off file.
#include "writeGrid2DOFF.h"
#include <fstream>
#include <iostream>
#include <stdexcept>
void WRITE_GRID2D_OFF::WriteHeader(std::ostream& file) const {
file << Header() << "\n";
}
void WRITE_GRID2D_OFF::WriteComment(std::ostream& file,
const std::string& msg) const
{
file << "# " << msg << "\n";
}
void WRITE_GRID2D_OFF::WriteNumElements(std::ostream& file,
const GRID2D_POINTS3D& grid2D) const
{
file << grid2D.NumPoints() << " "
<< grid2D.NumQuadrilaterals() << " 0\n";
}
void WRITE_GRID2D_OFF::WritePointCoordinates(std::ostream& file,
const GRID2D_POINTS3D& grid2D) const
{
for (int irow = 0; irow < grid2D.NumRows(); irow++) {
for (int jcol = 0; jcol < grid2D.NumCols(); jcol++) {
auto c = grid2D.Coord(irow, jcol);
file << c[0] << " " << c[1] << " " << c[2] << "\n";
}
}
}
void WRITE_GRID2D_OFF::WriteQuadrilaterals(std::ostream& file,
const GRID2D_POINTS3D& grid2D) const
{
if (grid2D.NumRows() < 2 || grid2D.NumCols() < 2) {
// Nothing to write.
return;
}
for (int irow = 0; irow < grid2D.NumRows() - 1; irow++) {
for (int icol = 0; icol < grid2D.NumCols() - 1; icol++) {
int iv0 = grid2D.PointIndex(irow, icol);
int iv1 = iv0 + 1;
int iv2 = iv1 + grid2D.NumCols();
int iv3 = iv0 + grid2D.NumCols();
file << "4 " << iv0 << " " << iv1
<< " " << iv2 << " " << iv3 << "\n";
}
}
}
void WRITE_GRID2D_OFF::Write(std::ostream& file,
const GRID2D_POINTS3D& grid2D,
const std::vector<std::string>& comment_list) const
{
WriteHeader(file);
for (const auto& comment : comment_list) {
WriteComment(file, comment);
}
WriteNumElements(file, grid2D);
WritePointCoordinates(file, grid2D);
file << "\n";
WriteQuadrilaterals(file, grid2D);
}
void WRITE_GRID2D_OFF::OpenAndWrite(
const std::string& filename,
const GRID2D_POINTS3D& grid2D,
const std::vector<std::string>& comment_list) const
{
try {
std::ofstream outfile(filename);
if (!outfile.is_open()) {
std::cerr << "Cannot open output file " << filename << ".\n";
throw std::runtime_error(
"Cannot open output file " + filename + " for writing.");
}
Write(outfile, grid2D, comment_list);
}
catch (const std::out_of_range& e) {
std::cerr << "Error writing file " << filename
<< ".\n " << e.what() << "\n";
throw;
}
catch (const std::runtime_error& e) {
std::cerr << "Error writing file " << filename
<< ".\n " << e.what() << "\n";
throw;
}
catch (const std::exception& e) {
std::cerr << "Error writing file " << filename
<< ".\n " << e.what() << "\n";
throw;
}
}

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// Functions to write grid2DPoints3D as a Geomview .off file.
#ifndef WRITE_GRID2D_OFF_H
#define WRITE_GRID2D_OFF_H
#include <iostream>
#include <string>
#include <vector>
#include "grid2DPoints3D.h"
// ********************************************************************************
// Class WRITE_GRID2D_OFF
// ********************************************************************************
/// A class for writing GRID2D_POINTS3D as a Geomview .off file.
class WRITE_GRID2D_OFF {
public:
const std::string OFF_HEADER = "OFF";
WRITE_GRID2D_OFF() {}
std::string Header() const { return OFF_HEADER; }
/// Write the OFF file header line.
void WriteHeader(std::ostream& file) const;
/// Write a comment line.
void WriteComment(std::ostream& file, const std::string& msg) const;
/// Write the counts: num_points, num_quads, 0 (edges).
void WriteNumElements(std::ostream& file,
const GRID2D_POINTS3D& grid2D) const;
/// Write the coordinates of all grid points.
void WritePointCoordinates(std::ostream& file,
const GRID2D_POINTS3D& grid2D) const;
/// Write the grid quadrilaterals.
void WriteQuadrilaterals(std::ostream& file,
const GRID2D_POINTS3D& grid2D) const;
/// Write grid2D to an open Geomview .off file stream.
void Write(std::ostream& file,
const GRID2D_POINTS3D& grid2D,
const std::vector<std::string>& comment_list) const;
/// Open filename and write grid2D in Geomview .off format.
void OpenAndWrite(const std::string& filename,
const GRID2D_POINTS3D& grid2D,
const std::vector<std::string>& comment_list) const;
};
#endif // WRITE_GRID2D_OFF_H