Basic mathematics

# Basic mathematics - Basic mathematics for geometric...

This preview shows pages 1–10. Sign up to view the full content.

Basic mathematics for geometric modeling

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Coordinate Reference Frames Cartesian Coordinate (2D) Polar coordinate x y (x, y) r θ
x P Y x y r θ θ r x y P Use trigonometric, polar cartesian x = r cos θ , y = r sin θ Cartesian polar r = x 2 + y 2 , θ = tan -1 (y/x)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3D cartesian coordinates x y z Right-handed 3D coordinate system z x y
POINT The simplest of geometric object. No length, width or thickness. Location in space Defined by a set of numbers (coordinates) e.g P = (x, y) or P = (x, y, z) Vertex of 2D/ 3D figure

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
distance and direction Does not have a fixed location in space Sometime called “displacement”. VECTOR
VECTOR Can define a vector as the difference between two point positions. x y P Q x1 x2 y1 y2 V V = Q – P = (x2 – x1, y2 – y1) = (Vx, Vy) Also can be expressed as V = Vx i + Vy j Component form

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
VECTOR : magnitude & direction Calculate magnitude using the Pythagoras theorem distance |V| = Vx 2 + Vy 2 Direction θ = tan -1 (Vy/Vx)
Example 1 If P(3, 6) and Q(6, 10). Write vector V in component form. Answer

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/11/2011 for the course MATH 110 taught by Professor Staff during the Winter '08 term at BYU.

### Page1 / 29

Basic mathematics - Basic mathematics for geometric...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online