# Keywords:

• dominant points
• consecutive vectors
• toothbrush shape
• distance metric
• smallest perpendicular distance

# Q1: How usual calculation of distance is done?

Minor DPs are deleted in approximation. A minor DP is a DP where the perpendicular distance between the point and the straight line is minimum.

a a
b


Here b is deleted when its distance to the line a-a is minimum.

The perpendicular distance is calculated using

[ d\~i~ = \sqrt{\frac{((x~i~ - x~a~) (y~b~ - y~a~) - (y~i~ - y~a~) (x~b~ -x~a~))^2^}{(x~a~ - x~b~)^2^ + (y~a~ - y~b~)^2^}} ]

for lines between points $p_a$ and $p_b$ and the point $p_i$.

# Q2: What is a toothbrush shape?

It's something like

aaaaaa
bbbbbbbbbbbbbbbbbbbbbb


Hence the toothbrush.

Though I don't get why is this particularly important.

# Q3: Which information is included in distance metric?

Angle acuteness is added to the information described above.

# Q4: How the distance metric differs from others?

It includes angle acuteness in the metric and the more acute the angle, the less likely it's removed from DP set.

# Q5: What's baseline for performance and how does this improve it?

As the number of DPs decrease, RMSE of the new metric decrease. For large number of DPs it doesn't matter much. (So performance penalty may not payoff)