grid1d 0.3.1

# Grid1D Decision Guide

This guide helps you make informed choices about which grid types, scalar types, and features to use in your application.

## Quick Decision Trees

### 🎯 Which Grid Type Should I Use?

```
START: What kind of spacing do I need?
│
├─ Equal spacing everywhere?
│  └─ ✅ Use Grid1DUniform
│     • O(1) point location
│     • Maximum performance
│     • Perfect for regular discretizations
│
├─ Custom/adaptive spacing?
│  └─ ✅ Use Grid1DNonUniform
│     • O(log n) point location
│     • Flexible point distribution
│     • Ideal for boundary layers, shock capturing
│
└─ Combining multiple grids?
   └─ ✅ Use Grid1DUnion
      • Combines grids from different physics
      • Maintains mappings to original grids
      • For multi-physics simulations
```

### 📐 Which Interval Type Should I Use?

```
START: What are your domain boundaries?
│
├─ Both endpoints are part of the domain?
│  └─ ✅ Use IntervalClosed [a, b]
│     • Most common choice
│     • Points at a and b are included
│     • Standard for boundary value problems
│
├─ Neither endpoint is part of the domain?
│  └─ ✅ Use IntervalOpen (a, b)
│     • Points strictly between a and b
│     • For open sets, strict inequalities
│     • Rare in practice
│
├─ Periodic or partition-friendly boundary?
│  ├─ Left closed, right open?
│  │  └─ ✅ Use IntervalLowerClosedUpperOpen [a, b)
│  │     • Common for periodic domains
│  │     • Non-overlapping partitions
│  │     • Example: [0, 2π) for angles
│  │
│  └─ Left open, right closed?
│     └─ ✅ Use IntervalLowerOpenUpperClosed (a, b]
│        • Asymmetric boundaries
│        • Less common
│
├─ Semi-infinite domain?
│  ├─ Bounded below only?
│  │  └─ ✅ Use IntervalLowerClosedUpperUnbounded [a, +∞)
│  │     • Example: time t ≥ 0
│  │     • Example: distance r ≥ 0
│  │
│  └─ Bounded above only?
│     └─ ✅ Use IntervalLowerUnboundedUpperClosed (-∞, b]
│        • Example: x ≤ 0
│
└─ Single point (degenerate)?
   └─ ✅ Use IntervalSingleton {a}
      • Zero-measure domain
      • Special case handling
```

### 🔢 Which Scalar Type Should I Use?

```
START: What are your priorities?
│
├─ Maximum performance, fully trusted inputs?
│  └─ ✅ Use f64
│     • Zero overhead
│     • Standard IEEE 754
│     • ⚠️  No validation - can propagate NaN/Inf
│
├─ Good performance + safety during development?
│  └─ ✅ Use RealNative64StrictFiniteInDebug (⭐ RECOMMENDED)
│     • Same as f64 in release builds
│     • Validates in debug builds
│     • Perfect development → production workflow
│
├─ Safety-critical application?
│  └─ ✅ Use RealNative64StrictFinite
│     • Always validates (small overhead ~5-10%)
│     • Guaranteed finite values
│     • For medical, aerospace, financial
│
└─ Need arbitrary precision?
   └─ ✅ Use RealRugStrictFinite<N>
      • N-bit precision (e.g., 256, 512, 1024)
      • For scientific computing, symbolic math
      • Requires `--features=rug`
```

## Detailed Comparison Tables

### Grid Type Comparison

| Feature | Grid1DUniform | Grid1DNonUniform | Grid1DUnion |
|---------|--------------|------------------|-------------|
| **Point Location** | O(1) analytical | O(log n) binary search | O(log n) on unified grid |
| **Memory Usage** | 8n + 40 bytes | 8n + 40 bytes | 8(n+m) + overhead |
| **Construction** | O(n) | O(n) | O(n+m) |
| **Best For** | Regular meshes, FDM | Adaptive meshes, FEM | Multi-physics coupling |
| **Spacing** | Uniform | Arbitrary | Combined |
| **Flexibility** | Low | High | Very High |
| **Performance** | ⚡⚡⚡ Excellent | ⚡⚡ Good | ⚡⚡ Good |

*Where n = number of points, m = points in second grid*

### Scalar Type Comparison

| Scalar Type | Validation | Debug | Release | Use Case |
|-------------|-----------|--------|---------|----------|
| **f64** | ❌ None | ⚡⚡⚡ | ⚡⚡⚡ | Trusted inputs, maximum speed |
| **RealNative64StrictFiniteInDebug** | ✅ Debug only | ⚡⚡ | ⚡⚡⚡ | **Recommended default** |
| **RealNative64StrictFinite** | ✅ Always | ⚡⚡ | ⚡⚡ | Safety-critical |
| **RealRugStrictFinite\<N\>** | ✅ Always | ⚡ | ⚡ | Arbitrary precision |

### Interval Type Selection

| Mathematical Need | Interval Type | Notation | Use Case |
|------------------|---------------|----------|----------|
| Include both endpoints | `IntervalClosed` | [a, b] | Standard bounded domains |
| Exclude both endpoints | `IntervalOpen` | (a, b) | Open sets, strict inequalities |
| Include left, exclude right | `IntervalLowerClosedUpperOpen` | [a, b) | Periodic domains, half-open ranges |
| Include right, exclude left | `IntervalLowerOpenUpperClosed` | (a, b] | Asymmetric boundaries |
| Unbounded above | `IntervalLowerClosedUpperUnbounded` | [a, +∞) | Semi-infinite domains |
| Unbounded below | `IntervalLowerUnboundedUpperClosed` | (-∞, b] | Semi-infinite domains |
| Single point | `IntervalSingleton` | {a} | Degenerate intervals |

### 🔀 Which Refinement Strategy Should I Use?

```
START: How do you want to refine your grid?
│
├─ Same refinement everywhere?
│  └─ ✅ Use refine_uniform()
│     • Every interval gets the same number of extra points
│     • Simple API: grid.refine_uniform(&num_extra_points)
│     • Best for: uniform quality improvement
│
├─ Different refinement in different regions?
│  └─ ✅ Use refine() with BTreeMap
│     • Specify extra points per interval ID
│     • Only refine where needed
│     • Best for: adaptive mesh refinement (AMR)
│
└─ Combining two existing grids?
   └─ ✅ Use Grid1DUnion instead
      • Not refinement, but unification
      • Preserves both original grid structures
      • Best for: multi-physics coupling
```

### 🔄 Grid Union vs Grid Refinement: When to Use Each?

```
START: What is your goal?
│
├─ Make current grid finer?
│  │
│  ├─ Uniformly finer everywhere?
│  │  └─ ✅ Use refine_uniform()
│  │
│  └─ Finer only in specific regions?
│     └─ ✅ Use refine() with BTreeMap
│
├─ Couple two independent grids?
│  └─ ✅ Use Grid1DUnion
│     • Both grids retain their identity
│     • Bidirectional mapping preserved
│     • For multi-physics data exchange
│
└─ Create grid from scratch with custom points?
   └─ ✅ Use Grid1D::try_from_sorted()
      • Direct construction from coordinates
      • Maximum flexibility
      • When refinement hierarchy not needed
```

| Feature | `refine_uniform()` | `refine()` | `Grid1DUnion` |
|---------|-------------------|------------|---------------|
| **Purpose** | Global refinement | Selective refinement | Grid coupling |
| **Tracks parent intervals** | ✅ Yes | ✅ Yes | ✅ Yes (both grids) |
| **Preserves original grid** | As parent | As parent | Both grids intact |
| **Best for** | h-refinement FEM | AMR, error-driven | Multi-physics |
| **Memory overhead** | Low | Low | Medium |
| **Complexity** | Simple | Medium | Higher |

### Refinement Strategy Examples

**Uniform refinement** - Every interval gets 2 extra points (→ 3 sub-intervals each):

```rust
use grid1d::{Grid1D, IntervalPartition, intervals::*, scalars::{NumIntervals, PositiveNumPoints1D}};
use try_create::TryNew;

let grid = Grid1D::uniform(IntervalClosed::new(0.0, 1.0), NumIntervals::try_new(4).unwrap());
// Original: 4 intervals

let refinement = grid.refine_uniform(&PositiveNumPoints1D::try_new(2).unwrap());
// Refined: 12 intervals (4 × 3)

// Track parent-child relationships
for (refined_id, original_id) in refinement.iter_refined_with_mapping() {
    println!("Refined interval {} came from original interval {}", 
             refined_id.as_ref(), original_id.as_ref());
}
```

**Selective refinement** - Only refine where needed (adaptive mesh refinement):

```rust
use grid1d::{Grid1D, IntervalPartition, intervals::*, scalars::{NumIntervals, PositiveNumPoints1D, IntervalId}};
use std::collections::BTreeMap;
use try_create::TryNew;

let grid = Grid1D::uniform(IntervalClosed::new(0.0, 1.0), NumIntervals::try_new(4).unwrap());

// Refine only intervals 0 and 2
let plan = BTreeMap::from([
    (IntervalId::new(0), PositiveNumPoints1D::try_new(3).unwrap()), // 4 sub-intervals
    (IntervalId::new(2), PositiveNumPoints1D::try_new(1).unwrap()), // 2 sub-intervals
]);

let refinement = grid.refine(&plan);
// Result: intervals 1 and 3 unchanged, 0 and 2 refined
```

**Grid union** - Couple two grids for multi-physics:

```rust
use grid1d::{Grid1D, Grid1DUnion, IntervalPartition, intervals::*, scalars::NumIntervals};
use try_create::TryNew;

// Flow solver: coarse grid
let flow_grid = Grid1D::uniform(
    IntervalClosed::new(0.0, 1.0), 
    NumIntervals::try_new(10).unwrap()
);

// Chemistry solver: fine grid in reaction zone
let chem_grid = Grid1D::uniform(
    IntervalClosed::new(0.0, 1.0), 
    NumIntervals::try_new(50).unwrap()
);

// Unified grid for coupling
let coupled = Grid1DUnion::try_new(&flow_grid, &chem_grid).unwrap();

// Transfer data between physics
for (unified_id, flow_id, chem_id) in coupled.iter_interval_mappings() {
    // Map solution from flow grid to chemistry grid and vice versa
}
```

## Use Case → Recommended Configuration

### Finite Difference Methods (Regular Mesh)

**Scenario**: Solving PDEs on uniform grids

```rust
// Recommended configuration
type Real = RealNative64StrictFiniteInDebug;  // Debug safety
type Domain = IntervalClosed<Real>;            // Closed boundaries

let grid = Grid1D::uniform(
    Domain::new(Real::try_new(0.0).unwrap(), Real::try_new(1.0).unwrap()),
    NumIntervals::try_new(1000).unwrap()
);
```

**Why?**

- ✅ Uniform grid: O(1) point location for maximum performance
- ✅ Debug validation: Catches NaN/Inf during development
- ✅ Closed interval: Standard for boundary value problems
- ✅ Release performance: Same as raw f64

### Finite Element Methods (Adaptive Mesh)

**Scenario**: FEM with mesh refinement in regions of interest

```rust
use grid1d::{Grid1D, IntervalPartition, intervals::*, scalars::{NumIntervals, PositiveNumPoints1D, IntervalId}};
use num_valid::RealNative64StrictFinite;
use std::collections::BTreeMap;
use try_create::TryNew;

// Recommended configuration
type Real = RealNative64StrictFinite;  // Always validated
type Domain = IntervalClosed<Real>;

// Start with coarse base mesh
let base_grid = Grid1D::uniform(
    Domain::new(Real::try_new(0.0).unwrap(), Real::try_new(1.0).unwrap()),
    NumIntervals::try_new(10).unwrap()
);

// Compute error estimator, identify intervals needing refinement
let error_threshold = 0.01;
let refinement_plan: BTreeMap<IntervalId, PositiveNumPoints1D> = (0..*base_grid.num_intervals().as_ref())
    .filter(|&i| estimate_error(i) > error_threshold)
    .map(|i| (IntervalId::new(i), PositiveNumPoints1D::try_new(1).unwrap()))
    .collect();

// Refine selectively where solution changes rapidly
let refined = base_grid.refine(&refinement_plan);

fn estimate_error(_interval: usize) -> f64 { 0.02 } // Placeholder
```

**Why?**

- ✅ Selective refinement: Only refine where errors are large
- ✅ Always validated: Prevents propagation of numerical errors
- ✅ Refinement tracking: Maintains parent-child relationships
- ✅ Flexible spacing: Optimal resolution where needed

### Computational Fluid Dynamics (Boundary Layers)

**Scenario**: Viscous flow with wall boundary layers

```rust
use grid1d::{Grid1D, intervals::*};
use num_valid::RealNative64StrictFiniteInDebug;
use sorted_vec::partial::SortedSet;

// Recommended configuration
type Real = RealNative64StrictFiniteInDebug;
type Domain = IntervalClosed<Real>;

// Generate boundary layer mesh with geometric stretching
fn create_boundary_layer_distribution(
    wall_position: f64,
    outer_position: f64,
    first_cell_height: f64,
    stretching_ratio: f64,
    max_points: usize,
) -> Vec<f64> {
    let mut coords = vec![wall_position];
    let mut y = wall_position;
    let mut dy = first_cell_height;
    
    for _ in 1..max_points {
        y += dy;
        if y >= outer_position {
            coords.push(outer_position);
            break;
        }
        coords.push(y);
        dy *= stretching_ratio;
    }
    coords
}

let coords = create_boundary_layer_distribution(0.0, 1.0, 0.001, 1.2, 50);

// Domain is inferred from first and last coordinates
let grid = Grid1D::<IntervalClosed<f64>>::try_from_sorted(
    SortedSet::from_unsorted(coords)
).unwrap();
```

**Why?**

- ✅ Non-uniform grid: Fine near wall, coarse in freestream
- ✅ Custom distribution: Precise control over point clustering
- ✅ Performance: Fast lookups even with non-uniform spacing
- ✅ Simplified API: Domain inferred from coordinates

### Multi-Physics Coupling

**Scenario**: Coupling fluid flow with chemical reactions

```rust
use grid1d::{Grid1D, Grid1DUnion, IntervalPartition, intervals::*, scalars::NumIntervals};
use num_valid::RealNative64StrictFinite;
use sorted_vec::partial::SortedSet;
use try_create::TryNew;

// Recommended configuration
type Real = RealNative64StrictFinite;  // Safety for complex coupling
type Domain = IntervalClosed<Real>;

// Flow grid: coarse global mesh
let flow_grid = Grid1D::uniform(
    Domain::new(Real::try_new(0.0).unwrap(), Real::try_new(1.0).unwrap()),
    NumIntervals::try_new(20).unwrap()
);

// Chemistry grid: fine mesh in reaction zone (non-uniform)
let chem_coords: Vec<f64> = (0..=100).map(|i| {
    let t = i as f64 / 100.0;
    // Cluster points near x=0.5 (reaction zone)
    0.5 + 0.5 * (std::f64::consts::PI * (t - 0.5)).tanh()
}).collect();

let chemistry_grid = Grid1D::<IntervalClosed<f64>>::try_from_sorted(
    SortedSet::from_unsorted(chem_coords)
).unwrap();

// Unified grid for data transfer
let coupled = Grid1DUnion::try_new(&flow_grid, &chemistry_grid).unwrap();

// Map between grids for data exchange
for (unified_id, flow_id, chem_id) in coupled.iter_interval_mappings() {
    // Transfer temperature from flow → chemistry
    // Transfer reaction rates from chemistry → flow
    println!("Unified {} maps to flow {}, chemistry {}", 
             unified_id.as_ref(), flow_id.as_ref(), chem_id.as_ref());
}
```

**Why?**

- ✅ Grid union: Preserves both discretizations
- ✅ Bidirectional mapping: Efficient data transfer
- ✅ Validated scalars: Prevents coupling instabilities
- ✅ Mixed grid types: Uniform flow + non-uniform chemistry

### High-Precision Scientific Computing

**Scenario**: Numerical analysis requiring exact arithmetic

```rust
#[cfg(feature = "rug")]
{
    // Recommended configuration
    type Real = RealRugStrictFinite<256>;  // 256-bit precision
    type Domain = IntervalClosed<Real>;
    
    let grid = Grid1D::uniform(
        Domain::new(
            Real::try_new(0.0).unwrap(),
            Real::try_new(1.0).unwrap()
        ),
        NumIntervals::try_new(100).unwrap()
    );
}
```

**Why?**

- ✅ Arbitrary precision: Eliminates rounding errors
- ✅ Validated: Maintains numerical integrity
- ✅ Same API: Easy to switch from f64

### Real-Time Applications

**Scenario**: Simulation loop with strict timing requirements

```rust
// Recommended configuration
type Real = f64;  // Maximum performance, no validation
type Domain = IntervalClosed<Real>;

let grid = Grid1D::uniform(
    Domain::new(0.0, 1.0),
    NumIntervals::try_new(1000).unwrap()
);

// In real-time loop
loop {
    // O(1) point location - predictable timing
    let interval_id = grid.find_interval_id_of_point(&sensor_value);
    // ... process ...
}
```

**Why?**

- ✅ Raw f64: Zero overhead, predictable performance
- ✅ Uniform grid: O(1) lookups, no branch prediction issues
- ✅ No validation: No runtime checks in critical path

## Performance Tuning Guidelines

### When to Choose Uniform Grid

✅ **Choose uniform grid when:**

- All intervals need equal spacing
- Maximum performance is critical
- Simple, regular domain discretization
- Point location happens frequently

❌ **Avoid uniform grid when:**

- Features occur at different scales
- Adaptive refinement is needed
- Boundary layer resolution required

### When to Choose Non-Uniform Grid

✅ **Choose non-uniform grid when:**

- Adaptive spacing is beneficial
- Multiple length scales present
- Boundary layer capture needed
- Features localized in space

❌ **Avoid non-uniform grid when:**

- Uniform spacing is sufficient
- Maximum performance is critical
- Simple regular problem

### When to Use Parallel Point Location

✅ **Use `find_intervals_for_points_parallel()` when:**

- Locating ≥1,000 points at once
- Running on multi-core systems
- Point location is a bottleneck
- Processing large datasets

❌ **Use sequential `find_intervals_for_points()` when:**

- Locating < 1,000 points
- Single-threaded environment required
- Need deterministic ordering
- Rayon overhead would dominate

**Performance guidance:**

| Points | Sequential | Parallel | Speedup |
|--------|------------|----------|------|
| 100 | ✅ Faster | ❌ Overhead | N/A |
| 1,000 | ≈ Equal | ≈ Equal | ~1× |
| 10,000 | Slower | ✅ Faster | ~3-4× |
| 100,000+ | Much slower | ✅ Much faster | ~6-8× |

### When to Use Grid Union

✅ **Use grid union when:**

- Coupling multiple physics
- Different solvers on different grids
- Need to preserve original grid structure
- Frequent data transfer between grids

❌ **Avoid grid union when:**

- Single physics problem
- Don't need grid mapping
- Memory is constrained

## Scalar Type Performance Impact

### Benchmarked Overheads (relative to f64)

| Operation | f64 | RealNative64StrictFiniteInDebug (Debug) | RealNative64StrictFiniteInDebug (Release) | RealNative64StrictFinite |
|-----------|-----|----------------------------------------|-------------------------------------------|--------------------------|
| Arithmetic | 1.0× | 1.5-2.0× | 1.0× | 1.05-1.10× |
| Comparison | 1.0× | 1.3-1.5× | 1.0× | 1.02-1.05× |
| Grid creation | 1.0× | 1.5× | 1.0× | 1.10× |
| Point location | 1.0× | 1.2× | 1.0× | 1.05× |

**Key takeaway**: `RealNative64StrictFiniteInDebug` has zero overhead in release builds.

## Migration Strategies

### From f64 to Validated Types

**Step 1**: Start with raw f64

```rust
let grid = Grid1D::uniform(
    IntervalClosed::new(0.0_f64, 1.0_f64),
    NumIntervals::try_new(100).unwrap()
);
```

**Step 2**: Add debug validation (no code changes needed in release!)

```rust
type Real = RealNative64StrictFiniteInDebug;
let grid = Grid1D::uniform(
    IntervalClosed::new(
        Real::try_new(0.0).unwrap(),
        Real::try_new(1.0).unwrap()
    ),
    NumIntervals::try_new(100).unwrap()
);
```

**Step 3**: If safety-critical, use always-validated

```rust
type Real = RealNative64StrictFinite;
// Same code as Step 2
```

### From Uniform to Non-Uniform

**Before** (uniform):

```rust
use grid1d::{Grid1D, intervals::*, scalars::NumIntervals};
use try_create::TryNew;

let grid = Grid1D::uniform(
    IntervalClosed::new(0.0, 1.0),
    NumIntervals::try_new(100).unwrap()
);
```

**After** (non-uniform with custom spacing):

```rust
use grid1d::{Grid1D, intervals::*};
use sorted_vec::partial::SortedSet;

fn generate_custom_distribution() -> Vec<f64> {
    // Example: cluster points near boundaries
    (0..=100).map(|i| {
        let t = i as f64 / 100.0;
        // Chebyshev-like distribution
        0.5 * (1.0 - (std::f64::consts::PI * t).cos())
    }).collect()
}

let coords = generate_custom_distribution();
// Domain is inferred from first and last coordinates
let grid = Grid1D::<IntervalClosed<f64>>::try_from_sorted(
    SortedSet::from_unsorted(coords)
).unwrap();
```

## Common Pitfalls and Solutions

### Pitfall 1: Using Wrong Grid Type

❌ **Wrong**:

```rust
use grid1d::{Grid1D, intervals::*};
use sorted_vec::partial::SortedSet;

// Using non-uniform grid when uniform would work
let coords: Vec<f64> = (0..=100).map(|i| i as f64 / 100.0).collect();
let grid = Grid1D::<IntervalClosed<f64>>::try_from_sorted(
    SortedSet::from_unsorted(coords)
).unwrap();  // O(log n) lookups - unnecessary overhead!
```

✅ **Correct**:

```rust
use grid1d::{Grid1D, intervals::*, scalars::NumIntervals};
use try_create::TryNew;

// Use uniform grid for better performance
let grid = Grid1D::uniform(
    IntervalClosed::new(0.0, 1.0),
    NumIntervals::try_new(100).unwrap()
);  // O(1) lookups!
```

### Pitfall 2: Over-validating in Performance-Critical Code

❌ **Wrong**:

```rust
type Real = RealNative64StrictFinite;  // Always validates

// In hot loop
for _ in 0..1_000_000 {
    let result = a + b;  // Validates every operation
}
```

✅ **Correct**:

```rust
type Real = RealNative64StrictFiniteInDebug;  // Validates only in debug

// In hot loop - no overhead in release
for _ in 0..1_000_000 {
    let result = a + b;  // Fast in release
}
```

### Pitfall 3: Forgetting to Handle Errors

❌ **Wrong**:

```rust
use grid1d::{Grid1D, intervals::*};
use sorted_vec::partial::SortedSet;

let coords = SortedSet::from_unsorted(vec![0.0, 0.5, 1.0]);
let grid = Grid1D::<IntervalClosed<f64>>::try_from_sorted(coords).unwrap();  // Panics on error!
```

✅ **Correct**:

```rust
use grid1d::{Grid1D, intervals::*};
use sorted_vec::partial::SortedSet;

let coords = SortedSet::from_unsorted(vec![0.0, 0.5, 1.0]);
let grid = Grid1D::<IntervalClosed<f64>>::try_from_sorted(coords)
    .map_err(|e| {
        eprintln!("Grid creation failed: {:?}", e);
        e
    })?;
```

### Pitfall 4: Using new() with Untrusted Input

❌ **Wrong**:

```rust
use grid1d::intervals::*;

// new() panics if lower > upper!
let user_input_lo = get_user_input(); // Could be anything
let user_input_hi = get_user_input();
let interval = IntervalClosed::new(user_input_lo, user_input_hi); // 💥 May panic!

fn get_user_input() -> f64 { 5.0 } // Placeholder
```

✅ **Correct**:

```rust
use grid1d::intervals::*;

let user_input_lo = get_user_input();
let user_input_hi = get_user_input();
let interval = IntervalClosed::try_new(user_input_lo, user_input_hi)
    .map_err(|e| format!("Invalid interval: {:?}", e))?;

fn get_user_input() -> f64 { 5.0 } // Placeholder
```

## Summary Recommendations

### For Most Users (⭐ Recommended)

```rust
use grid1d::{Grid1D, intervals::*, scalars::NumIntervals};
use num_valid::RealNative64StrictFiniteInDebug;
use try_create::TryNew;

type Real = RealNative64StrictFiniteInDebug;
type Domain = IntervalClosed<Real>;

// Uniform grid for regular problems
let grid = Grid1D::uniform(
    Domain::new(Real::try_new(0.0).unwrap(), Real::try_new(1.0).unwrap()),
    NumIntervals::try_new(100).unwrap()
);
```

**This gives you**:

- ✅ Maximum performance in release builds
- ✅ Safety validation during development
- ✅ O(1) point location for uniform grids
- ✅ Easy to change if needs evolve

### Quick Reference Card

| Need | Use |
|------|-----|
| Regular mesh, maximum speed | `Grid1DUniform` + `f64` |
| **Most applications** | **`Grid1DUniform` + `RealNative64StrictFiniteInDebug`** |
| Adaptive mesh | `Grid1DNonUniform` + `RealNative64StrictFiniteInDebug` |
| Safety-critical | Any grid + `RealNative64StrictFinite` |
| Multi-physics | `Grid1DUnion` + `RealNative64StrictFinite` |
| High precision | Any grid + `RealRugStrictFinite<N>` |
| Periodic domains | Any grid + `IntervalLowerClosedUpperOpen` |

---

For more details, see:

- [Complete Tutorial](./TUTORIAL.md)
- [API Documentation](https://docs.rs/grid1d)
- [README](./README.md)