# A Survey of Implicit Constraints in Primitives

## Contents

## Types of Implicit Parameters[edit]

At the level of constraint networks, calculations are done in terms of Variables or indpendent real values / floating point numbers. But in the construction of geometry these are clustered together in terms of implicit parameters. Typical implicit parameters are

**Vectors**- A 3 dimensional vector is a 3-tuple which is used to hold direction as well as magnitude. In BRL-CAD primitives, they may represent- Radius vectors ( Center of a sphere)
- Direction vectors (Direction of a plane)

## Types of Implicit Constraints[edit]

An enumeration of the set of contraints observed in the primitives below

**Modulus Comparison**: Comparison of the modulus of a vector to a real number ( 0 for non-negativity ) or the modulus of another vector**Perpendicularity of Vectors**

## Implict Constraints by Primitive[edit]

### ell (Ellipse)[edit]

Ellipse is built using the Center (radius vector V) and 3 Vectors (A, B, C st. |A| = radius) 2 types: Non-negativity/Modulus comparison, Perpendicularity Constraints:

- |A| > 0
- |B| > 0
- |C| > 0
- A.B = 0
- B.C = 0
- C.A = 0

### rec (Right elliptical cylinder)[edit]

3 types: Non-negativity/Modulus comparison, Perpendicularity, Vector equality

Constraints:

- |H| > 0
- |A| > 0
- |B| > 0
- A = C
- B = D
- A.B = 0
- H.A = 0
- H.B = 0

### rhc (Right hyperbolic cylinder)[edit]

3 types: Non-negativity/Modulus comparison, Perpendicularity

Constraints:

- |H| > 0
- |B| > 0
- |R| > 0
- H • B = 0
- c > 0
- |B| ≥ c

### rpc (Right parabolic cylinder)[edit]

2 types: Non-negativity/Modulus comparison, Perpendicularity

Constraints:

- |H| > 0
- |B| > 0
- |R| > 0
- H.B = 0

### sph (Sphere)[edit]

Sphere is a particular case of the ellipse

Constraints: 2 types: Modulus comparison, Perpendicularity

- |A| > 0
- |B| > 0
- |C| > 0
- |A| = |B|
- |A| = |C|
- |B| = |C|
- A.B = 0
- B.C = 0
- C.A = 0

### tgc (Truncated General Cone)[edit]

Constraints: 5 types: Modulus comparison, Logical Combination, Perpendicularity, Non-planarity, Parallelism

- |H| > 0
- |A| & |B| not zero together
- |B| & |D| not zero togehter
- |A|*|B| and |C|*|D| not zero together
- H is nonplanar to AB plane
- A.B = 0
- C.D = 0
- A || C ( A is parallel to C )

### tor (Torus)[edit]

Tor is built using the following input fields

V V from origin to center H Radius Vector, Normal to plane of torus. |H| = R2 A, B perpindicular, to CENTER of torus. |A|==|B|==R1 F5, F6 perpindicular, for inner edge (unused) F7, F8 perpindicular, for outer edge (unused)

Constraints: 2 types: Modulus comparison, Perpendicularity

- |A| = |B|
- A.B = 0
- B.H = 0
- H.A = 0
- |H| > 0
- |H| < |A|