Watch this slide to learn: 1) Types of quantities? 2) Representation of matrix in Euclidean space? 3) Vector ( in terms of matrix )? 4) Unit vector 5) Operations on vector in MATLAB: 6) Parametric equation of line 7) Cross product 8) Vector dot product 9) Polygon 10) Area of polygon 11) Center of polygon 12) Collinear points

1. SPATIAL DATA MODELING
Lecture no 5
Presented by:
Sadia Sheikh

2. • Types of quantities?
• Representation of matrix in Euclidean space?
• Vector ( in terms of matrix )?
• 1) Unit vector
• Operations on vector in MATLAB:
• Parametric equation of line
• Cross product
• Vector dot product
• Polygon
• Area of polygon
• Center of polygon
• Collinear points

3. •Scalar magnitude
•Vector magnitude+direction

4. EUCLIDEAN SPACE
• R2
= 4i+3j
• R3
=4i+3j+5k
• In system vector are expressed in terms of Matrics of
n*1 in which n is the (Rn
) power of R.

5. VECTOR
• Can be seen as a line segment, point from reference point
• Can be expressed in the form of displacement
• Has many shapes
• Mostly take origin as a reference point
• Vector define in term of (i,j,k)

6. UNIT VECTOR
• In mathematics, a unit vector is a vector whose
length is 1 (the unit length). A unit vector is often
denoted by a lowercase letter with a "hat" ,like
this: (pronounced "i-hat").
u
u
u

ˆ
uˆu

7. CROSS PRODUCT
• The cross product of two vectors a and b is denoted by a × b.
• Definition of the cross product can also be represented by the
determinant of a formal matrix:
kji
kji
vvv
uuu
kji
vu 


8. PARAMETRIC EQUATION OF LINE
• A straight line is defined by a linear equation whose
general form is
• In vector this is represented in the form of Parametric
equation
• It is a line having its origin at xo and it is parallel to
vector v
0 cbyax
vtxx o


Reference Point Scalar Quantity
Vector

9. VECTOR DOT PRODUCT
jjii uvuvuv .
• Formulla

10. ORTHOGONAL
• Orthogonality occurs when two things can vary
independently, they are uncorrelated, or they are
perpendicular.
• Dot product is used to know orthogonal

11. CROSS PRODUCT
• The cross product of two vectors a and b is denoted by a × b.
• Definition of the cross product can also be represented by the
determinant of a formal matrix:
kji
kji
vvv
uuu
kji
vu 


12. PARAMETRIC EQUATION OF LINE
• A straight line is defined by a linear equation whose
general form is
• In vector this is represented in the form of Parametric
equation
• It is a line having its origin at xo and it is parallel to
vector v
0 cbyax
vtxx o


Reference Point Scalar Quantity
Vector

13. POLYGON
• Area of triangle in Euclidean geometry
Area=width*length
If three points are required then convert into matrix form.
Area=1/2*IAI
A=

14. AREA OF POLYGON
• Similarly:
)()((
2
1
Area 11
1
0



  iii
n
i
i xyyx

15. CENTER OF POLYGON
• Center of Polygon:
)()(
6
1
110 1     iiiii iix xyyxxx
A
C
)()(
6
1
110 1     iiiii ii xyyxyy
A
Cy

16. COLLINEAR POINTS
• Three or more points P1,P2 ,P3 , are said to be collinear if they
lie on a single straight line

17. THNAK YOU!