fix: Fortran engine use_marker/alpha header passthrough + case04 Moon orbit fix

- engines/fortran/main.f90:
  - 新增 use_marker 和 alpha_str 的读取、传递、写入 display.txt header
  - 新增 json_get_alpha 函数兼容 JSON 单值或 6 元数组
- engines/release/: 引擎校准缓存 & fortran.json 参数
- examples/case04/: 修正月球位置 (11.5→10.5) 和速度 (526→647),
  地月距缩至希尔半径以内 (0.5 < 1.0), 新增希尔半径验证说明
- examples/Readme.html: case04/case09 描述更新

engines/fortran/main.f90

@@ -21,6 +21,8 @@ program dynamics_f90
     integer :: driving_force
     double precision :: gravity_strength
     character(len=32) :: method
+    integer :: use_marker
+    character(len=512) :: alpha_str
     double precision :: t0, t1, elapsed, tw
 
     ! 原子数据
@@ -71,7 +73,8 @@ program dynamics_f90
     ! 读取 param.json
     call read_params(param_path, box_a, NT, DT, NSTEP, warmup_steps, method, G, B, &
                      gravity_field, gravity_interaction, &
-                     elastic_force, damping_force, gravity_strength, driving_force)
+                     elastic_force, damping_force, gravity_strength, driving_force, &
+                     use_marker, alpha_str)
 
     ! 读取 coord.txt
     call read_coord(input_dir, n_atoms, atom_ids, masses, radii, pos_0, vel_0, fixed)
@@ -201,7 +204,8 @@ program dynamics_f90
                            traj_x, traj_y, traj_z, traj_vx, traj_vy, traj_vz, &
                            NT, DT, NSTEP, warmup_steps, method, G, B, &
                            n_bonds, gravity_field, elastic_force, damping_force, &
-                           driving_force, box_a, gravity_strength)
+                           driving_force, box_a, gravity_strength, &
+                           use_marker, alpha_str)
 
     call cpu_time(t1)
     elapsed = t1 - t0
@@ -228,15 +232,17 @@ contains
 ! ========================================================================
 subroutine read_params(path, box_a, NT, DT, NSTEP, warmup_steps, method, G, B, &
                        gravity_field, gravity_interaction, &
-                       elastic_force, damping_force, gravity_strength, driving_force)
+                       elastic_force, damping_force, gravity_strength, driving_force, &
+                       use_marker, alpha_str)
     character(len=*), intent(in) :: path
     double precision, intent(out) :: box_a, DT, G(3), B(3), gravity_strength
     integer, intent(out) :: NT, NSTEP, warmup_steps
     integer, intent(out) :: gravity_field, gravity_interaction, elastic_force, damping_force, driving_force
-    character(len=*), intent(out) :: method
+    integer, intent(out) :: use_marker
+    character(len=*), intent(out) :: method, alpha_str
     character(len=8096) :: buf
     character(len=256) :: line
-    integer :: u, ios
+    integer :: u, ios, i
 
     box_a = 10.0d0; NT = 10000; DT = 0.001d0; NSTEP = 100; warmup_steps = 0
     method = 'leapfrog'
@@ -244,6 +250,8 @@ subroutine read_params(path, box_a, NT, DT, NSTEP, warmup_steps, method, G, B, &
     gravity_field = 1; gravity_interaction = 0
     elastic_force = 1; damping_force = 0; gravity_strength = 1.0d0
     driving_force = 0
+    use_marker = 0
+    alpha_str = '0.2'
 
     open(newunit=u, file=trim(path), status='old', action='read', iostat=ios)
     if (ios /= 0) then
@@ -274,6 +282,8 @@ subroutine read_params(path, box_a, NT, DT, NSTEP, warmup_steps, method, G, B, &
     damping_force       = json_get_int(buf, 'damping_force', 0)
     gravity_strength    = json_get_double(buf, 'gravity_strength', 1.0d0)
     driving_force       = json_get_int(buf, 'driving_force', 0)
+    use_marker          = json_get_int(buf, 'use_marker', 0)
+    call json_get_alpha(buf, 'alpha', alpha_str)
 end subroutine read_params
 
 ! ========================================================================
@@ -323,6 +333,55 @@ subroutine json_get_double3(buf, key, vals)
     end do
 end subroutine json_get_double3
 
+! 读取 alpha：兼容单值 (0.2) 或 6 元数组 [0.0,0.0,0.0,0.0,0.0,0.0]
+! 输出为逗号分隔字符串，与 draw.py 的解析格式一致
+subroutine json_get_alpha(buf, key, val)
+    character(len=*), intent(in) :: buf, key
+    character(len=*), intent(out) :: val
+    double precision :: d6(6)
+    integer :: p, i, ios
+    character(len=32) :: tmp
+    val = '0.2'
+    p = index(buf, '"' // key // '"')
+    if (p == 0) return
+    p = index(buf(p:), ':') + p
+    ! skip whitespace
+    do while (p <= len(buf) .and. (buf(p:p) == ':' .or. buf(p:p) == ' ' &
+           .or. buf(p:p) == char(9) .or. buf(p:p) == char(10)))
+        p = p + 1
+    end do
+    if (buf(p:p) == '[') then
+        ! 6 元数组
+        d6 = 0.2d0
+        p = p + 1
+        do i = 1, 6
+            do while (p <= len(buf) .and. (buf(p:p) == ' ' .or. buf(p:p) == ',' &
+                   .or. buf(p:p) == char(9) .or. buf(p:p) == char(10)))
+                p = p + 1
+            end do
+            if (p > len(buf) .or. buf(p:p) == ']') exit
+            read(buf(p:), *, iostat=ios) d6(i)
+            if (ios /= 0) exit
+            do while (p <= len(buf) .and. buf(p:p) /= ',' .and. buf(p:p) /= ']')
+                p = p + 1
+            end do
+        end do
+        val = ''
+        do i = 1, 6
+            write(tmp, '(f0.6)') d6(i)
+            if (i > 1) val = trim(val) // ','
+            val = trim(val) // trim(tmp)
+        end do
+    else
+        ! 单值标量
+        read(buf(p:), *, iostat=ios) d6(1)
+        if (ios == 0) then
+            write(tmp, '(f0.6)') d6(1)
+            val = trim(tmp)
+        end if
+    end if
+end subroutine json_get_alpha
+
 ! 从 JSON 中读取字符串值
 subroutine json_get_string(buf, key, val)
     character(len=*), intent(in) :: buf, key
@@ -999,10 +1058,12 @@ subroutine write_display_txt(outdir, n_frames, nat, aid, &
                               tx, ty, tz, tvx, tvy, tvz, &
                               NT, DT, NSTEP, warmup, method, G, B, &
                               nb, gravity_field, elastic_force, damping_force, &
-                              driving_force, box_a, gravity_strength)
+                              driving_force, box_a, gravity_strength, &
-    character(len=*), intent(in) :: outdir, method
+                              use_marker, alpha_str)
+    character(len=*), intent(in) :: outdir, method, alpha_str
     integer, intent(in) :: n_frames, nat, NT, NSTEP, warmup, nb
     integer, intent(in) :: gravity_field, elastic_force, damping_force, driving_force
+    integer, intent(in) :: use_marker
     integer, intent(in) :: aid(nat)
     double precision, intent(in) :: tx(n_frames, nat), ty(n_frames, nat), tz(n_frames, nat)
     double precision, intent(in) :: tvx(n_frames, nat), tvy(n_frames, nat), tvz(n_frames, nat)
@@ -1051,6 +1112,8 @@ subroutine write_display_txt(outdir, n_frames, nat, aid, &
     write(buf, '("Y_MAX: ", g0)')  box_a;  write(u, '(a)') trim(buf)
     write(buf, '("Z_MIN: ", g0)') -box_a;  write(u, '(a)') trim(buf)
     write(buf, '("Z_MAX: ", g0)')  box_a;  write(u, '(a)') trim(buf)
+    write(u, '("use_marker: ", i0)')  use_marker
+    write(u, '("alpha: ", a)')         trim(alpha_str)
 
     ! ── frame data ────────────────────────────────────────────────────────
     do f = 1, n_frames

engines/release/_calib_c.json

@@ -1 +1 @@
-{"n_atoms": 40, "nt": 10000, "step_time": 0.00015027170181274412}
+{"n_atoms": 40, "nt": 10000, "step_time": 3.113259077072144e-05}

engines/release/_calib_fortran.json

@@ -0,0 +1 @@
+{"n_atoms": 40, "nt": 200000, "step_time": 0.0002908185601234436}

engines/release/fortran.json

@@ -0,0 +1,51 @@
+{
+  "box_a": 300.0,
+  "NT": 200000,
+  "DT": 0.001,
+  "NSTEP": 100,
+  "warmup_steps": 0,
+  "method": "leapfrog",
+  "G": [
+    0.0,
+    0.0,
+    0.0
+  ],
+  "B": [
+    0.005,
+    0.0,
+    0.005
+  ],
+  "gravity_field": 0,
+  "gravity_interaction": 0,
+  "elastic_force": 1,
+  "damping_force": 0,
+  "gravity_strength": 1.0,
+  "driving_force": 1,
+  "save_trajectory": 0,
+  "alpha": [
+    0.0,
+    0.0,
+    0.0,
+    0.0,
+    0.0,
+    0.0
+  ],
+  "ball_radius": 0.5,
+  "ball_color": [
+    0.2,
+    0.6,
+    0.9
+  ],
+  "box_color": [
+    0.8,
+    0.8,
+    0.85
+  ],
+  "use_marker": 1,
+  "camera_distance": 60.0,
+  "camera_elevation": 0.0,
+  "camera_azimuth": 0.0,
+  "camera_center_x": 30.0,
+  "camera_center_y": 0.0,
+  "camera_center_z": 0.0
+}

examples/Readme.html

@@ -210,7 +210,7 @@
 <div class="case-card">
   <span class="num">04</span>
   <h3>日地月系统（稳定）</h3>
-  <p>三体系统稳定椭圆轨道</p>
+  <p>三体系统稳定轨道，经希尔半径检验</p>
   <div class="meta">
     <span class="tag tag-python">Python</span>
     <span class="tag tag-gravity">万有引力</span>
@@ -263,7 +263,7 @@
 <div class="case-card">
   <span class="num">09</span>
   <h3>一维链纵波·Fortran 引擎</h3>
-  <p>Fortran 引擎驱动的纵波传播测试</p>
+  <p>Fortran 引擎驱动的纵波，GPU 实例化渲染</p>
   <div class="meta">
     <span class="tag tag-fortran">Fortran</span>
     <span class="tag tag-spring">弹簧</span>
@@ -323,8 +323,8 @@
     <li class="tag tag-python">Python 引擎</li>
     <li class="tag tag-gravity">万有引力</li>
   </ul>
-  <p>与 case03 相同的三体系统，但采用恰当的初始条件，地球和月球维持稳定的椭圆轨道运动。</p>
+  <p>与 case03 相同的三体系统，但采用恰当的初始条件：地球置于近日点（$r=10$），$v_z=520$ 接近圆轨道；月球缩至希尔半径（$r_H\approx1.0$）以内的 $r=0.5$，相对速度 $v_{\text{rel}}\approx127$，确保月球被地球稳定束缚。</p>
-  <div class="highlight">✅ 与 case03 对比学习：初始条件对数值稳定性的影响</div>
+  <div class="highlight">✅ 与 case03 对比学习：初始条件对数值稳定性的影响。地月距 0.5 在地球希尔半径以内，满足稳定性条件</div>
 </div>
 
 <div class="detail-card">
@@ -377,8 +377,8 @@
     <li class="tag tag-spring">弹簧键力</li>
     <li class="tag tag-drive">驱动力</li>
   </ul>
-  <p>40 原子沿 x 轴排列，Fortran 引擎驱动的纵波传播测试。验证 Fortran 引擎的输出兼容性。</p>
+  <p>40 原子沿 x 轴排列，Fortran 引擎驱动的纵波传播测试。使用 <code>use_marker: 1</code>（GPU 实例化 Marker 模式）加速渲染，验证 Fortran 引擎与其他引擎的输出兼容性。</p>
-  <div class="highlight">🔧 Fortran 引擎兼容性验证，T_total=200, NSTEP=100</div>
+  <div class="highlight">🔧 Fortran 引擎兼容性验证，T_total=200, NSTEP=100。Marker 模式下 40 原子以 GPU 点精灵渲染，帧率高</div>
 </div>
 
 <div class="detail-card">

examples/case04/Readme.html

@@ -337,10 +337,14 @@ MathJax = {
   <tr><th>天体</th><th>质量</th><th>位置 $(x,y,z)$</th><th>速度 $(v_x,v_y,v_z)$</th><th>固定约束</th></tr>
   <tr><td>太阳</td><td>$27\,000$</td><td>$(0,0,0)$</td><td>$(0,0,0)$</td><td>全部固定</td></tr>
   <tr><td>地球</td><td>$81$</td><td>$(10,0,0)$</td><td>$(0,0,520)$</td><td>无</td></tr>
-  <tr><td>月球</td><td>$1$</td><td>$(11.5,0,0)$</td><td>$(0,0,526)$</td><td>无</td></tr>
+  <tr><td>月球</td><td>$1$</td><td>$(10.5,0,0)$</td><td>$(0,0,647)$</td><td>无</td></tr>
 </table>
 
-<p>地球在 $z$ 方向获得初速度 $v=520$，产生绕太阳的轨道运动；月球在地球基础上附加 $v=6$ 的绕地速度，形成绕地球的微小轨道。速度由圆形轨道公式 $v = \sqrt{G_{\text{eff}} M / r}$ 计算，其中 $G_{\text{eff}} = \text{gravity\_strength} = 100$。</p>
+<p>地球在 $z$ 方向获得初速度 $v=520$，产生绕太阳的轨道运动（接近圆轨道）；月球在地球基础上附加 $v\approx127$ 的绕地速度，形成绕地球的轨道。速度由圆形轨道公式 $v = \sqrt{G_{\text{eff}} M / r}$ 计算，其中 $G_{\text{eff}} = \text{gravity\_strength} = 100$。</p>
+
+<div class="highlight">
+  <strong>验证</strong>：地球速度 $v_\oplus = \sqrt{100 \times 27\,000 / 10} \approx 519.6$，设 520 正确。月球相对速度 $v_{\text{rel}} = \sqrt{100 \times 81 / 0.5} \approx 127.3$，设 127 正确。地月距离 0.5 在地球希尔半径 $r_H \approx 10 \times (81 / 81\,000)^{1/3} \approx 1.0$ 之内，可确保轨道稳定。
+</div>
 
 <h2>五、使用方法</h2>
 
@@ -372,9 +376,10 @@ MathJax = {
 
 <ul>
   <li>太阳真实质量为月球 $27\,100\,000$ 倍，模拟中缩至 $27\,000$ 倍以保持数值稳定（$1/1000$）</li>
-  <li>轨道半径未按真实比例缩放（真实日地距是地月距的 389 倍，模拟中仅为 6.7 倍）</li>
+  <li>轨道半径未按真实比例缩放（真实日地距是地月距的 389 倍，模拟中约为 20 倍，受希尔半径约束，月球已尽可能放远）</li>
   <li>未考虑月球轨道倾角（真实地月轨道有约 5° 的倾角）</li>
   <li>leapfrog 算法为能量守恒的辛积分器，长期稳定，但步长过大时仍可能偏离真实轨道</li>
+  <li>太阳固定不动可作为教学简化，但严格三体模拟中应让所有天体在质心系中自由运动</li>
 </ul>
 
 </div>
@@ -424,18 +429,19 @@ MathJax = {
     ctx.strokeStyle = '#c9d1d9';
     ctx.lineWidth = 1.5;
     ctx.stroke();
-    // 箭头
+    // 箭头（左端：椭圆中心 cx+f）
     ctx.beginPath();
-    ctx.moveTo(cx - f + 6, aY - 4);
+    ctx.moveTo(cx + f + 6, aY - 4);
-    ctx.lineTo(cx - f, aY);
+    ctx.lineTo(cx + f, aY);
-    ctx.lineTo(cx - f + 6, aY + 4);
+    ctx.lineTo(cx + f + 6, aY + 4);
     ctx.strokeStyle = '#c9d1d9';
     ctx.lineWidth = 1.5;
     ctx.stroke();
+    // 箭头（右端：右顶点 cx+f+A）
     ctx.beginPath();
-    ctx.moveTo(cx - f + A - 6, aY - 4);
+    ctx.moveTo(cx + f + A - 6, aY - 4);
-    ctx.lineTo(cx - f + A, aY);
+    ctx.lineTo(cx + f + A, aY);
-    ctx.lineTo(cx - f + A - 6, aY + 4);
+    ctx.lineTo(cx + f + A - 6, aY + 4);
     ctx.strokeStyle = '#c9d1d9';
     ctx.lineWidth = 1.5;
     ctx.stroke();
@@ -453,17 +459,19 @@ MathJax = {
     ctx.strokeStyle = '#d29922';
     ctx.lineWidth = 1.5;
     ctx.stroke();
+    // 箭头（左端：左焦点=cx 太阳）
     ctx.beginPath();
-    ctx.moveTo(cx - f + 5, cY - 4);
+    ctx.moveTo(cx + 5, cY - 4);
-    ctx.lineTo(cx - f, cY);
+    ctx.lineTo(cx, cY);
-    ctx.lineTo(cx - f + 5, cY + 4);
+    ctx.lineTo(cx + 5, cY + 4);
     ctx.strokeStyle = '#d29922';
     ctx.lineWidth = 1.5;
     ctx.stroke();
+    // 箭头（右端：椭圆中心 cx+f）
     ctx.beginPath();
-    ctx.moveTo(cx - 5, cY - 4);
+    ctx.moveTo(cx + f - 5, cY - 4);
-    ctx.lineTo(cx, cY);
+    ctx.lineTo(cx + f, cY);
-    ctx.lineTo(cx - 5, cY + 4);
+    ctx.lineTo(cx + f - 5, cY + 4);
     ctx.strokeStyle = '#d29922';
     ctx.lineWidth = 1.5;
     ctx.stroke();

examples/case04/input/coord.txt

@@ -1,4 +1,4 @@
 n mass  radius    x   y   z   vx   vy   vz fix_x fix_y fix_z
-1 27000 2.0   0 0 0  0  0  0    1 1 1
+1 27000    1.0    0   0   0    0    0    0     1     1     1
-2 81    0.5   10 0 0 0  0  520  0 0 0
+2    81    0.2   10   0   0    0    0  520     0     0     0
-3 1     0.3   11.5 0 0 0 0 526  0 0 0
+3     1    0.1   10.5 0   0    0    0  647     0     0     0

examples/case04/input/input.txt

@@ -74,7 +74,7 @@ T_total: 10.0
 NSTEP: 2
 
 # ── 时间步长 ──────────────────────────────────
-DT:    0.001         # 时间步长 (s)
+DT:    0.0001         # 时间步长 (s)
 
 # 抽帧范围：只保存 [sample_start, sample_end) 区间内的帧
 sample_start: null        # null 表示从头开始（帧索引从 0 起）