Bezier Demo Missing Features - Implementation Status

Overview

This document tracks the implementation status of features needed for the original complex Bezier surface MATLAB demo to work natively in XDL.

Completed Features ✓

1. NCHOOSEK Function (Binomial Coefficient)

Status: ✅ COMPLETED

Implementation:

  • Added nchoosek(n, k) function in xdl-stdlib/src/math.rs

  • Computes binomial coefficient: C(n,k) = n! / (k! * (n-k)!)
  • Uses iterative computation to avoid overflow
  • Registered in stdlib function registry

Test:

print, nchoosek(5, 2)    ; Output: 10
print, nchoosek(10, 3)   ; Output: 120

Files Modified:

  • xdl-stdlib/src/math.rs - Added function implementation
  • xdl-stdlib/src/lib.rs - Registered function

Pending Features 🔨

2. 2D Array Indexing

Status: ⏳ TODO

Current Limitation:

arr = fltarr(10, 10)
val = arr[i, j]  ; ❌ ERROR: Multi-dimensional indexing requires nested array

Workaround:

arr = fltarr(100)  ; Flatten to 1D
idx = i * 10 + j
val = arr[idx]     ; ✅ Works

Implementation Requirements:

  • Extend lexer/parser to handle comma-separated indices
  • Modify interpreter’s array access logic to support multi-dimensional indexing
  • Update XdlValue to track array dimensions/shape
  • Implement row-major or column-major indexing (GDL uses column-major)

Estimated Complexity: HIGH (requires significant parser and runtime changes)

3. MESHGRID Function

Status: ⏳ TODO

Purpose: Create 2D coordinate matrices from 1D coordinate vectors for plotting and surface generation.

Expected Behavior:

x = [1, 2, 3]
y = [4, 5]
[X, Y] = meshgrid(x, y)
% X = [[1, 2, 3],
%      [1, 2, 3]]
% Y = [[4, 4, 4],
%      [5, 5, 5]]

Current Workaround:

; Manual coordinate grid generation
for i = 0, nx-1 do begin
  for j = 0, ny-1 do begin
    U[idx] = x_vals[i]
    V[idx] = y_vals[j]
    idx = idx + 1
  end
endfor
end
endfor

Implementation Requirements:

  • Add meshgrid(x, y) function to array.rs
  • Handle returning multiple values (X and Y matrices)
  • Implement proper 2D array representation

Estimated Complexity: MEDIUM

4. Line Continuation ($)

Status: ⏳ TODO

Current Limitation:

cp_z = [[0.0, 0.5, 0.5, 0.0], $    ; ❌ Parser error
        [0.5, 1.5, 1.5, 0.5], $
        [0.5, 1.5, 1.5, 0.5]]

Workaround:

; Split into separate lines/variables
cp_z_row1 = [0.0, 0.5, 0.5, 0.0]   ; ✅ Works
cp_z_row2 = [0.5, 1.5, 1.5, 0.5]
cp_z_row3 = [0.5, 1.5, 1.5, 0.5]

Implementation Requirements:

  • Modify lexer to recognize $ as line continuation
  • Join continued lines before tokenization
  • Handle nested array literals across multiple lines

Estimated Complexity: LOW-MEDIUM

5. Nested Function Definitions

Status: ⏳ TODO

Current Limitation:

function result = bernstein(i, n, t)
    result = nchoosek(n, i) * (t.^i) .* (1-t).^(n-i);
end

Workaround:

; Expand function inline or create separate PRO file
u_w0 = (1-u)^3
u_w1 = 3.0 * (1-u)^2 * u
u_w2 = 3.0 * (1-u) * u^2
u_w3 = u^3

Implementation Requirements:

  • Add function definition support to parser (MATLAB function or GDL PRO/FUNCTION)
  • Implement function scope and local variables
  • Handle function return values
  • Support nested function definitions within scripts

Estimated Complexity: VERY HIGH (requires significant language feature additions)

6. Complex Number Support

Status: ⏳ TODO

Current Limitation:

z = -1-1i;        ; ❌ Not supported
w = 2 + 3i;       ; ❌ Not supported

Workaround:

; Use real numbers only or separate real/imaginary parts
real_part = -1.0
imag_part = -1.0

Implementation Requirements:

  • Add Complex type to XdlValue enum
  • Implement imaginary unit (i or j)
  • Override arithmetic operators for complex numbers
  • Add functions: real(), imag(), abs(), angle(), conj()
  • Support complex array operations

Estimated Complexity: HIGH

Priority Recommendations

Short Term (Quick Wins)

  1. Line Continuation ($) - Improves code readability
  2. MESHGRID - Commonly used, moderate effort

Medium Term

  1. 2D Array Indexing - Major quality of life improvement
  2. Complex Numbers - Expands application domains

Long Term

  1. Nested Functions - Full MATLAB/GDL compatibility
  2. Advanced Features - Additional plotting options (subplot, figure, etc.)

Testing Strategy

Each implemented feature should include:

  1. Unit tests in the relevant module
  2. Integration test in examples/
  3. Documentation update in relevant README
  4. Entry in CHANGELOG.md

References

Last Updated: 2025-10-23