This algorithm smooths a given G-code toolpath by iteratively removing points that lie too close to the line segment formed by their preceding and succeeding points. It's crucial for reducing vibration and wear on CNC ma...

The `smoothPath` function takes a list of `Point` objects representing the original toolpath and a `tolerance` value. It iterates through the path, considering each point `current` along with its `previous` (last added to smoothed path) and `next` (from original path) points. The core logic relies on `distanceToSegment`, which calculates the shortest distance from `current` to the line segment defined by `previous` and `next`. If this distance is less than or equal to the `tolerance`, the `current` point is considered redundant and is skipped, effectively simplifying the path. The first and last points are always preserved to maintain the path's start and end locations. The time complexity is O(N) where N is the number of points in the original path, as each point is visited once. The space complexity is O(N) in the worst case, as the smoothed path could retain all original points. Edge cases handled include paths with fewer than 3 points (no smoothing possible), and the `distanceToSegment` function correctly handles cases where the segment endpoints are identical. The invariant maintained is that the `smoothed` path always represents a valid, simplified version of the original path up to the current iteration.

Function smoothPath(path, tolerance): If path has less than 3 points, return path. Initialize smoothed_path with the first point of path. For each point 'current' from the second to the second-to-last point in path: Let...

This algorithm calculates the compensated toolpath point for CNC machining, implementing the logic behind G41 (cutter compensation left) and G42 (cutter compensation right) commands. It determines where the tool center s...

The `calculateCompensatedPoint` function takes the `current` point, the `prev` and `next` points defining the toolpath segment, the `radius` of the tool, and the `compType` (G41 or G42). First, it checks for invalid inputs like a non-positive radius or a zero-length segment, returning the `current` point unchanged in such cases. It then calculates the normalized vector representing the direction of the toolpath segment from `prev` to `next`. A perpendicular vector is derived from this segment vector; its direction depends on `compType`. For G41, the perpendicular vector points to the left of the tool's travel direction, and for G42, it points to the right. This perpendicular vector is scaled by the tool `radius` to produce an offset vector. Finally, this offset vector is added to the `current` point to yield the `compensatedPoint`. The time complexity is O(1) as it performs a fixed number of arithmetic operations. The space complexity is also O(1). Edge cases handled include zero radius and zero-length segments. A key invariant is that the compensated point lies on a line perpendicular to the toolpath segment, offset by the tool radius, on the correct side determined by G41/G42.

Function calculateCompensatedPoint(current, prev, next, radius, compType): If radius <= 0 or segment (prev, next) has zero length, return current. Calculate segment vector (next - prev). Normalize segment vector to get u...

This program simulates a basic drilling cycle for a CNC machine. It takes depth, feed rate, and spindle speed as input. The `MainDrillCycle` function validates these parameters, ensuring they are positive and within reas...

The algorithm focuses on parameter validation and sequential execution of drilling steps. The `MainDrillCycle` function acts as the entry point, ensuring robust input by checking for non-positive values for depth, feed, and spindle speed. If invalid values are detected, it assigns safe defaults and logs a warning. This prevents potential errors or unsafe operations. The `PerformDrill` function then simulates the actual drilling process, including spindle start, feed motion, retraction, and spindle stop. The use of helper functions promotes modularity and readability. The time complexity is O(1) as it involves a fixed number of operations and no loops or recursion. Space complexity is also O(1) as it uses a constant amount of memory.

PROGRAM BasicDrill FUNCTION MainDrillCycle(depth, feed, spindleSpeed) IF depth <= 0 THEN depth = 1.0 PRINT "Warning: Depth was non-positive, defaulting to 1.0" END IF IF feed <= 0 THEN feed = 100.0 PRINT "Warning: Feed w...

This program simulates an adaptive pocket machining cycle for CNC. It calculates a dynamic feed rate based on a target chip load and estimated material engagement, ensuring optimal cutting performance and tool life. The...

The algorithm implements adaptive feed control within a pocket machining context. The `MainPocketCycle` function orchestrates the process, validating input parameters like pocket points, depth, and spindle speed. It then iterates through the pocket's vertices, calculating the distance to the next point. For each segment, it estimates material engagement and uses the `CalculateAdaptiveFeed` helper to determine a feed rate that aims for a `TARGET_CHIP_LOAD`. The `ClampFeed` function ensures the calculated feed stays within safe `MIN_FEED_RATE` and `MAX_FEED_RATE` limits. This adaptive strategy prevents tool breakage from excessive load and maintains efficiency by not undercutting. Time complexity is O(N), where N is the number of pocket points, due to the loop. Space complexity is O(1) as it uses a fixed number of variables.

PROGRAM AdaptivePocketing CONST MAX_FEED_RATE, MIN_FEED_RATE, TARGET_CHIP_LOAD, TOOL_DIAMETER, TOOL_RADIUS TYPE Point { X, Y } FUNCTION MainPocketCycle(pocketPoints, depth, spindleSpeed) VALIDATE pocketPoints, depth, spi...

This program simulates a simple linear interpolation movement on a CNC machine. It takes target X and Y coordinates and a feed rate as input. The `PerformLinearMove` function validates the feed rate, ensuring it's positi...

The algorithm performs a single linear interpolation. The `PerformLinearMove` function is the core, taking target coordinates and feed rate. It includes a basic validation for the feed rate, defaulting to a safe value if it's non-positive. The primary action is printing a descriptive message simulating the machine's movement. This function is deterministic and has no loops or complex logic. Time complexity is O(1) as it involves a fixed sequence of operations. Space complexity is also O(1) due to constant memory usage.

PROGRAM LinearMove FUNCTION PerformLinearMove(xTarget, yTarget, feedRate) IF feedRate <= 0.0 THEN PRINT "Warning: Feed rate is non-positive. Defaulting to 200.0." feedRate = 200.0 END IF PRINT "Moving linearly to X: " +...

This program simulates the generation of a helical milling path, commonly used for creating pockets or large holes in CNC machining. The `GenerateHelixPath` function takes parameters like the center coordinates, initial...

The algorithm generates a series of linear segments that approximate a helical path. The `GenerateHelixPath` function validates input parameters such as initial radius, depth, spindle speed, and feed rate. It calculates the `helixPitch` based on a factor of the estimated tool diameter and then validates this pitch against `MIN_PITCH` and `MAX_PITCH`. The core logic involves a loop that iterates to create segments. For each segment, it calculates the start and end X, Y coordinates based on the current angle and radius, and the Z coordinate based on the accumulated depth and pitch. The number of steps is determined to ensure the path covers the required depth and makes at least one full revolution if possible. Time complexity is O(D/P), where D is the depth and P is the pitch, as the number of segments is proportional to the depth divided by the pitch. Space complexity is O(D/P) to store the generated segments.

PROGRAM HelicalPocketMilling CONST HELIX_PITCH_FACTOR, MIN_PITCH, MAX_PITCH, MIN_RADIUS TYPE HelixSegment { StartX, StartY, StartZ, EndX, EndY, EndZ, FeedRate } FUNCTION GenerateHelixPath(centerX, centerY, initialRadius,...

This program defines a sophisticated machining subroutine with extensive parameter validation and error handling. It accepts a `OperationParams` struct containing various machining parameters like tool diameter, spindle...

The algorithm focuses on robust parameter validation and structured output for a machining subroutine. The `ExecuteMachiningSubroutine` function takes a `OperationParams` struct and returns an `OperationResult` struct. It performs checks for positive values, range constraints, and valid enumerated types for each parameter. Invalid parameters immediately halt execution and return an error result. Warnings are issued for potentially suboptimal parameters. The core logic simulates outcomes based on parameter combinations, demonstrating conditional execution. The use of structs for input and output parameters enhances organization and readability. Time complexity is O(1) as it involves a fixed number of checks and operations, regardless of input values. Space complexity is O(1) for storing parameters and results.

PROGRAM AdvancedSubroutine TYPE OperationParams { ToolDiameter, SpindleSpeed, FeedRate, Depth, MaxAngle, OperationType, EnableCoolant } TYPE OperationResult { Success, Message, ActualDepth, ToolWear } FUNCTION ExecuteMac...

This program simulates a probing cycle to accurately measure the center of a circular feature on a CNC machine. It utilizes a `MeasureCircleCenter` function that takes the pocket radius and spindle speed as input. The co...

The algorithm implements a geometric approach to finding the center of a circle using a probing cycle. The `MeasureCircleCenter` function orchestrates the process, validating inputs and calling `ProbePoint` three times at 120-degree intervals. `ProbePoint` simulates the physical act of probing, including approach, measurement, and retraction, with a check for probe angle errors. The crucial part is `CalculateCircleCenter`, which takes three points and applies a geometric formula derived from perpendicular bisectors to find the center. This method is robust for finding circle centers. Time complexity is O(1) because the number of probes (3) and calculations is fixed, irrespective of the pocket size. Space complexity is O(1) for storing points and results.

PROGRAM ProbeCircleCenter CONST PROBE_DIAMETER, PROBE_RADIUS, APPROACH_DISTANCE, RETRACT_DISTANCE, MAX_PROBE_ANGLE_ERROR TYPE Point { X, Y } TYPE ProbeResult { Success, CenterX, CenterY, Message } FUNCTION MeasureCircleC...