This G-code generator smooths a series of linear path points using cubic Bezier curves. It takes an array of points, the number of segments to use for approximating each Bezier curve, and the feed rate as input. The func...

The `SmoothPathGCode` function generates G-code for a smoothed toolpath. It first defines a helper function `CalculateBezierPoint` which computes a point on a cubic Bezier curve given four control points and a parameter `t` (0 to 1). The main function validates that there are at least two points. It then moves the tool to a safe height, then to the first point, and descends to the cutting depth. For each segment between consecutive points in the input array, it defines four control points for a cubic Bezier curve. The control points are approximated here by using the start and end points and simple offsets derived from the segment's direction. It then iterates `numSegmentsPerCurve` times, calculating and outputting G-code commands for each intermediate point along the Bezier curve. The time complexity is O(N*S), where N is the number of input points and S is `numSegmentsPerCurve`, due to the nested loops. The space complexity is O(1) as it uses a fixed amount of memory for variables. Edge cases like fewer than two points are handled by returning an error. The approximation of control points is a simplification; a more advanced implementation would calculate tangents more rigorously.

FUNCTION CalculateBezierPoint(p0, p1, p2, p3, t): Calculate intermediate values for (1-t)^3, 3*(1-t)^2*t, 3*(1-t)*t^2, t^3 Calculate x and y coordinates using the cubic Bezier formula RETURN {x, y} END FUNCTION FUNCTION...

This algorithm implements a collision detection mechanism for CNC toolpaths. It checks if a linear move (defined by two points) intersects with a rectangular obstacle (defined by a bounding box). This is a fundamental co...

The `checkCollision` function determines if a tool's movement from `p1` to `p2` will intersect with an `obstacle` bounding box. It first uses `isPointInsideBox` to check if either the start or end point of the toolpath lies within the obstacle. If not, it calls `lineSegmentIntersectsBox` to perform a more rigorous check. `lineSegmentIntersectsBox` implements the Liang-Barsky line clipping algorithm, which is efficient for clipping a line segment against a rectangular window. It calculates parameters `t` representing the intersection points along the line segment relative to its endpoints. If the calculated `t` values indicate an intersection within the segment's bounds (0 to 1), it returns `true`. The time complexity is O(1) because the number of operations is constant, regardless of the input points or box dimensions. The space complexity is also O(1). Edge cases handled include endpoints inside the box, lines parallel to box edges (both inside and outside), and correctly ordered box coordinates. The algorithm's correctness relies on the established geometric principles of line-rectangle intersection.

FUNCTION checkCollision(p1, p2, obstacle): IF isPointInsideBox(p1, obstacle) OR isPointInsideBox(p2, obstacle): RETURN true RETURN lineSegmentIntersectsBox(p1, p2, obstacle) FUNCTION lineSegmentIntersectsBox(p1, p2, box)...

This algorithm automates the generation of G-code for drilling holes arranged in a circular pattern. It calculates the precise X and Y coordinates for each hole based on the circle's center, radius, and the desired numbe...

The `generateCircularDrillPattern` function produces G-code for drilling holes in a circle. It begins with standard G-code setup commands (`G17`, `G21`, `G90`) and moves to a safe Z height. The core of the algorithm is a loop that iterates `numHoles` times. In each iteration, it calculates the `currentAngle` for the hole using `2 * PI / numHoles`. Trigonometric functions (`math.Cos` and `math.Sin`) are then used to determine the `currentX` and `currentY` coordinates based on the `centerX`, `centerY`, `radius`, and `currentAngle`. Similar to the linear drill cycle, it generates `G0` moves to the hole's XY position, `G1` to plunge to `zDepth`, and `G0` to retract to the safe Z height. The time complexity is O(n), where n is `numHoles`, as each hole requires a fixed set of G-code commands. The space complexity is O(n) for storing the generated G-code strings. Edge cases like 0, 1, or 3 holes are handled correctly by the loop and angle calculation. The use of `math.Cos` and `math.Sin` ensures accurate placement of holes on the circle's circumference.

FUNCTION generateCircularDrillPattern(centerX, centerY, radius, numHoles, zDepth): commands = empty list of strings zPosition = 5.0 // Safe Z height ADD "G17" TO commands ADD "G21" TO commands ADD "G90" TO commands ADD "...

This algorithm generates a sequence of G-code commands to perform a linear drilling operation. It simulates a custom canned cycle by outputting commands for rapid moves to position, plunging to depth, and retracting. Thi...

The `generateLinearDrillCycle` function creates a list of G-code strings. It starts by setting common G-code modes like `G17` (XY plane), `G21` (metric units), and `G90` (absolute positioning). It then moves to a safe Z height. The core logic is a loop that iterates `numHoles` times. In each iteration, it calculates the `currentX` coordinate based on the `startX`, `spacing`, and loop index `i`. It then generates a `G0` (rapid move) command to the calculated `X,Y` position, followed by a `G1` (linear feed) command to plunge to `zDepth` at a specified feed rate. Finally, it retracts to the safe Z height using `G0`. After the loop, it adds commands to return to origin. The time complexity is O(n), where n is `numHoles`, as each hole requires a constant number of G-code commands. The space complexity is O(n) to store the generated G-code strings. Edge cases like 0 or 1 hole are handled correctly by the loop structure.

FUNCTION generateLinearDrillCycle(startX, startY, numHoles, spacing, zDepth): commands = empty list of strings zPosition = 5.0 // Safe Z height ADD "G17" TO commands ADD "G21" TO commands ADD "G90" TO commands ADD "G0 Z"...