Orientation
Vectors

The Frame and Handedness Are Defined

The candidate canonical frame is:

+x = Panoris = East
-x = Panvel = West
+y = Pankor = North
-y = Panvath = South

The planar frame is right-handed. Positive rotation is counterclockwise when viewed from the positive normal. The canonical zero direction is Panoris.

Pankor Is Exactly +y

Reference Vectors shall prove that canonical Pankor corresponds exactly to the positive y-axis of the Survey frame.

Presentation layers may label, rotate, or render the frame differently, but they may not alter the canonical mathematical meaning of Pankor.

Panvath Is Exactly -y

Reference Vectors shall prove that canonical Panvath corresponds exactly to the negative y-axis and is the exact opposed direction to Pankor.

Local or user-facing orientation conventions shall not redefine that relationship.

Panoris Is Exactly +x and the Zero Direction

The corpus shall prove that Panoris corresponds exactly to the positive x-axis of the canonical frame.

Panoris also serves as the canonical zero direction from which positive rotational orientation is interpreted.

Panvel Is Exactly -x

Reference Vectors shall prove that Panvel corresponds exactly to the negative x-axis and is the exact opposed direction to Panoris.

Derived views may mirror or rotate presentation, but canonical Panvel remains fixed within the Survey frame.

Canonical Oppositions Are Exact

The corpus shall demonstrate:

Pankor ↔ Panvath
Panoris ↔ Panvel

These are exact axis oppositions in the canonical frame and do not depend upon a future choice of named angular unit.

The Canonical Frame Is Right-Handed

Reference Vectors shall include ordered Point triples and basis cases sufficient to prove the permanent right-handed orientation of the canonical frame.

Exact determinant sign shall distinguish positive orientation, negative orientation, and collinearity without tolerance or floating-point approximation.

Turn Direction Is Exactly Testable

For ordered Points A, B, and C, the exact orientation determinant:

orient(A,B,C) = (Bx-Ax)(Cy-Ay) - (By-Ay)(Cx-Ax)

shall classify the turn deterministically as positive, negative, or collinear.

These vectors directly support geometry validation, segment intersection, SCPE normalization, and traversal orientation.

Positive Rotation Is Counterclockwise

Reference Vectors shall prove the selected positive rotational convention using cardinal and orientation-predicate cases that do not require a final angular unit.

Viewed from the positive normal, a positive turn proceeds counterclockwise from Panoris toward Pankor.

Allowed Transformations Must Preserve Handedness

Where the candidate mathematics permit orientation-preserving uniform affine placement, vectors shall prove that positive uniform scale and translation preserve canonical orientation.

Nonuniform scaling, shear, and reflection are not part of that placement model. They shall not be treated as equivalent canonical transformations.

Reflection Is Not Canonical Orientation Preservation

A reflected or mirrored presentation may exist at a higher layer, but reflection reverses handedness and therefore cannot silently become an equivalent canonical Survey transformation.

Reference Vectors shall distinguish presentation reflection from preservation of canonical orientation truth.

General Rotation Is Not Yet Fully Closed

Arbitrary exact rotation may map rational-coordinate Points to non-rational coordinates. The candidate Specification has therefore not yet closed a universal exact rotation representation compatible with CRPC.

Reference Vectors shall not publish arbitrary-angle rotated coordinate results as final canonical outputs until the Specification defines the exact result type and angular representation.

Orientation Semantics Do Not Require Premature Unit Selection

The canonical frame, handedness, zero direction, opposed directions, determinant orientation, and positive-turn convention are already testable.

The final angular unit remains open. Reference Vectors shall therefore avoid inventing degrees, radians, turns, or another canonical unit unless and until the Specification selects one.

Defined Orientation Semantics Must Reproduce Exactly

Independent conforming implementations shall return the same canonical direction, handedness, determinant sign, and supported transformation result for identical inputs under the same governing Specification.

A mismatch indicates implementation defect, Specification ambiguity, version incompatibility, fixture defect, or an orientation operation tested beyond the current mathematical closure.

Orientation Is Partly Executable Without a Final Angular Unit

The original page deferred nearly the entire corpus because positive rotation, handedness, and angular mathematics were all unresolved. That is no longer the current standing.

The frame, native directions, handedness, zero direction, determinant orientation, and positive rotational convention are now candidate-defined and testable. The unresolved work is concentrated in arbitrary rotation and angular-unit representation. Reference Vectors shall advance on the solved orientation semantics without inventing the remaining mathematics.

Referenced Requirements

Orientation Vectors will derive especially from Requirements Findings #10, #38–#43, #50, #53, #67–#68, #74, and #78–#83.