dpas

DPAS: Decimal Positional Angle System

A representational framework for angular orientation based on decimal semantics.

Abstract

Classical angle systems (Degrees, Radians) are essential for analytic geometry but often lack semantic alignment with the decimal positional notation we use daily. The Decimal Positional Angle System (DPAS) proposes a labeling scheme where orthogonal transitions correspond to decimal digit capacity (0–9, 10–19, etc.).

This is not a replacement for trigonometric calculation but a conceptual overlay designed for robotics, UI/UX, and educational clarity.

The Core Concept: "Decimal Overflow"

In DPAS, a full rotation is divided into 40 Macro Units, distributed across 4 orthogonal domains (quadrants). This mirrors the "tens" digit logic:

Domain (Quadrant)	DPAS Macro Range	Classic Degrees	Tens Digit Indicator
I (X+, Y+)	0.0 – 9.9	0° – 90°	0x (Single Digit)
II (X-, Y+)	10.0 – 19.9	90° – 180°	1x
III (X-, Y-)	20.0 – 29.9	180° – 270°	2x
IV (X+, Y-)	30.0 – 39.9	270° – 360°	3x

Features

• Macro Scale (0-40): Ideal for high-level logic and state machines.
• Micro Scale (0-400): Decimal subdivision for finer precision.
• Zero Overhead: Purely a representational layer; preserves all trigonometric identities.

Python Implementation

The included dpas.py provides a robust class for converting and handling DPAS values.

Installation

Just copy dpas.py into your project. No external dependencies required.

Usage

from dpas import DPAS

# 1. Convert from Degrees
angle = DPAS(195, mode='degrees')

print(f"Macro Value: {angle.macro}")  # Output: 21.66...
print(f"Domain: {angle.domain}")      # Output: 3 (Because it's in the 20s)

# 2. Check State Logic
if angle.domain == 3:
    print("System is in the 3rd Quadrant (South-West)")

# 3. Convert back
print(f"Back to Degrees: {angle.degrees}")