Unit-5
Circular Arc Generation using DDA Algorithm
The equation for an arc in the angle parameters can be given as.
x = Rcos cos θ + x0
y = Rsin sin θ + y0
Where (x_0, y_0) is the centre of curvature and R is the radius of arc.
Differentiating above equation
dx = −Rsin sin θdθ
dy = Rcosθdθ
We can solve for R costheta and R sintheta as follows
R cos θ = x − x0
R sin θ = y − y0
Substituting values we get
dx = −(y − y0 )dθ
dy = (x − x0 )dθ
x2 = x1 + dx = x1 − (y1 − y0 )dθ
y2 = y1 + dy = y1 + (x2 − x0 )dθ
dθ = Min(0.01, 1/(3.2 ∗ (∣x − x0 ∣ + ∣y − y0 ∣)))
Unit-5 1
Unit-5
Circular Arc Generation using DDA Algorithm
The equation for an arc in the angle parameters can be given as.
x = Rcos cos θ + x0
y = Rsin sin θ + y0
Where (x_0, y_0) is the centre of curvature and R is the radius of arc.
Differentiating above equation
dx = −Rsin sin θdθ
dy = Rcosθdθ
We can solve for R costheta and R sintheta as follows
R cos θ = x − x0
R sin θ = y − y0
Substituting values we get
dx = −(y − y0 )dθ
dy = (x − x0 )dθ
x2 = x1 + dx = x1 − (y1 − y0 )dθ
y2 = y1 + dy = y1 + (x2 − x0 )dθ
dθ = Min(0.01, 1/(3.2 ∗ (∣x − x0 ∣ + ∣y − y0 ∣)))
Unit-5 1
