Add more examples

Signed-off-by: Slendi <slendi@socopon.com>

examples/projection.cpp

@@ -0,0 +1,214 @@
+#include <algorithm>
+#include <cmath>
+#include <cstdint>
+#include <iostream>
+#include <print>
+#include <string>
+#include <vector>
+
+#if defined(_WIN32)
+#include <Windows.h>
+#endif
+
+#include <smath.hpp>
+using smath::Vec2;
+
+enum Color : uint8_t {
+  CLR_NONE = 0,  // default
+  CLR_AXES = 90, // bright black (gray)
+  CLR_A = 32,    // green
+  CLR_B = 33,    // yellow
+  CLR_P = 35,    // magenta
+  CLR_DOT = 36   // cyan
+};
+
+struct Cell {
+  char ch{' '};
+  uint8_t color{CLR_NONE};
+  int prio{0};
+};
+
+struct Canvas {
+  int w, h;
+  std::vector<Cell> pix;
+  Canvas(int W, int H) : w(W), h(H), pix(W * H) {}
+
+  void put(int x, int y, char c, int prio, uint8_t color) {
+    if (x < 0 || x >= w || y < 0 || y >= h)
+      return;
+    Cell &cell = pix[y * w + x];
+    if (prio >= cell.prio) {
+      cell.ch = c;
+      cell.prio = prio;
+      cell.color = color;
+    }
+  }
+  void hline(int y, char c, int prio, uint8_t color) {
+    for (int x = 0; x < w; ++x)
+      put(x, y, c, prio, color);
+  }
+  void vline(int x, char c, int prio, uint8_t color) {
+    for (int y = 0; y < h; ++y)
+      put(x, y, c, prio, color);
+  }
+
+  void line_dir(int x0, int y0, int x1, int y1, int prio, uint8_t color) {
+    int dx = std::abs(x1 - x0), sx = x0 < x1 ? 1 : -1;
+    int dy = -std::abs(y1 - y0), sy = y0 < y1 ? 1 : -1;
+    int err = dx + dy;
+
+    int px = x0, py = y0;
+    put(px, py, '+', prio, color);
+
+    while (true) {
+      if (px == x1 && py == y1)
+        break;
+      int e2 = 2 * err;
+      int nx = px, ny = py;
+      if (e2 >= dy) {
+        err += dy;
+        nx += sx;
+      }
+      if (e2 <= dx) {
+        err += dx;
+        ny += sy;
+      }
+
+      int sdx = nx - px;
+      int sdy = ny - py;
+      int adx = std::abs(sdx);
+      int ady = std::abs(sdy);
+      char g;
+      if (adx >= 2 * ady)
+        g = '-';
+      else if (ady >= 2 * adx)
+        g = '|';
+      else
+        g = ((sdx > 0 && sdy > 0) || (sdx < 0 && sdy < 0)) ? '\\' : '/';
+
+      put(nx, ny, g, prio, color);
+      px = nx;
+      py = ny;
+    }
+  }
+
+  void flush() const {
+    uint8_t cur = 255;
+    for (int y = 0; y < h; ++y) {
+      for (int x = 0; x < w; ++x) {
+        const Cell &c = pix[y * w + x];
+        if (c.color != cur) {
+          if (c.color == CLR_NONE)
+            std::print("\x1b[0m");
+          else
+            std::print("\x1b[{}m", c.color);
+          cur = c.color;
+        }
+        std::print("{}", c.ch);
+      }
+      std::println("");
+    }
+    std::print("\x1b[0m");
+  }
+};
+
+struct Mapper {
+  int W, H;
+  double scale;
+  int cx, cy;
+  Mapper(int w, int h, double s) : W(w), H(h), scale(s), cx(w / 2), cy(h / 2) {}
+  std::pair<int, int> map(Vec2 v) const {
+    int x = cx + (int)std::llround(v.x() * scale);
+    int y = cy - (int)std::llround(v.y() * scale);
+    return {x, y};
+  }
+};
+
+int main() {
+#if defined(_WIN32)
+  HANDLE h = GetStdHandle(STD_OUTPUT_HANDLE);
+  if (h != INVALID_HANDLE_VALUE) {
+    DWORD m;
+    if (GetConsoleMode(h, &m))
+      SetConsoleMode(h, m | ENABLE_VIRTUAL_TERMINAL_PROCESSING);
+  }
+#endif
+
+  std::print("Enter vector a (ax ay): ");
+  double ax, ay;
+  if (!(std::cin >> ax >> ay))
+    return 0;
+  std::print("Enter vector b (bx by): ");
+  double bx, by;
+  if (!(std::cin >> bx >> by))
+    return 0;
+
+  Vec2 a{(float)ax, (float)ay};
+  Vec2 b{(float)bx, (float)by};
+  Vec2 p = a.project_onto(b);
+
+  std::println("\nResults:");
+  std::println("a = {}", a);
+  std::println("b = {}", b);
+  std::println("proj_b(a) = p = {}", p);
+  std::println("|a|={}  |b|={}  |p|={}", a.magnitude(), b.magnitude(),
+               p.magnitude());
+  double dot = a.dot(b);
+  double ang = (a.magnitude() > 0 && b.magnitude() > 0)
+                   ? std::acos(std::clamp(dot / (a.magnitude() * b.magnitude()),
+                                          -1.0, 1.0)) *
+                         180.0 / M_PI
+                   : 0.0;
+  std::println("a·b={}  angle(a,b)={} deg\n", dot, ang);
+
+  const int W = 73, H = 33;
+  double maxr = std::max({(double)a.magnitude(), (double)b.magnitude(),
+                          (double)p.magnitude(), 1.0});
+  double usable = 0.45 * std::min(W, H);
+  double scale = usable / maxr;
+
+  Canvas cvs(W, H);
+  Mapper mp(W, H, scale);
+
+  int pr_axes = 1;
+  auto [cx, cy] = mp.map({0, 0});
+  cvs.hline(H / 2, '-', pr_axes, CLR_AXES);
+  cvs.vline(W / 2, '|', pr_axes, CLR_AXES);
+  cvs.put(W / 2, H / 2, 'O', pr_axes + 1, CLR_AXES);
+
+  auto [ox, oy] = mp.map({0, 0});
+  auto [ax1, ay1] = mp.map(a);
+  auto [bx1, by1] = mp.map(b);
+  auto [px1, py1] = mp.map(p);
+
+  int pr_a = 3, pr_b = 3, pr_p = 4;
+
+  cvs.line_dir(ox, oy, ax1, ay1, pr_a, CLR_A);
+  cvs.line_dir(ox, oy, bx1, by1, pr_b, CLR_B);
+  cvs.line_dir(ox, oy, px1, py1, pr_p, CLR_P);
+
+  if (!a.approx_equal(p) && b.magnitude() > 0) {
+    int steps = std::max(std::abs(ax1 - px1), std::abs(ay1 - py1));
+    for (int i = 0; i <= steps; ++i) {
+      double t = steps ? double(i) / steps : 0.0;
+      int x = (int)std::llround(px1 + t * (ax1 - px1));
+      int y = (int)std::llround(py1 + t * (ay1 - py1));
+      if (i % 2 == 0)
+        cvs.put(x, y, '.', 2, CLR_DOT);
+    }
+  }
+
+  auto place_label = [&](Vec2 v, const char *txt, uint8_t c, int pr) {
+    auto tip = mp.map(v * 1.05f);
+    for (int i = 0; txt[i]; ++i)
+      cvs.put(tip.first + i, tip.second, txt[i], pr, c);
+  };
+  place_label(a, "A", CLR_A, pr_a + 1);
+  place_label(b, "B", CLR_B, pr_b + 1);
+  place_label(p, "P", CLR_P, pr_p + 1);
+
+  std::println("Legend: axes(gray), a(green), b(yellow), p=proj(magenta), "
+               "dotted=cross-perp\n");
+  cvs.flush();
+  return 0;
+}

examples/random_steps.cpp

@@ -0,0 +1,43 @@
+/*
+ * smath - Single-file linear algebra math library for C++23.
+ *
+ * Copyright 2025 Slendi <slendi@socopon.com>
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * You can define the following macros to change functionality:
+ * - SMATH_IMPLICIT_CONVERSIONS
+ */
+
+#include <print>
+#include <random>
+
+#include <smath.hpp>
+
+auto main() -> int {
+  using namespace smath;
+
+  Vec2d point;
+  std::random_device rd;
+  std::mt19937 rng{rd()};
+  std::uniform_real_distribution<> dis(-5, 5);
+  int i = 0;
+  do {
+    Vec2d add{dis(rng), dis(rng)};
+    auto const n = point + add;
+    std::println("{}: {:.2f} + {:.2f} -> {:.2f}", i, point, add, n);
+    point = n;
+
+    i++;
+  } while (i < 15);
+}

include/smath.hpp

@@ -1,4 +1,5 @@
-/* smath - Single-file linear algebra math library for C++23.
+/*
+ * smath - Single-file linear algebra math library for C++23.
  *
  * Copyright 2025 Slendi <slendi@socopon.com>
  *