You can use BSplineFunction:
cps1 = {{8, 5}, {0, 0}, {10, 1}}; Graphics[{Thick, Red, Line[BSplineFunction[cps1] /@ Subdivide[0, 1/2, 50]], Blue, Line[BSplineFunction[cps1] /@ Subdivide[1/2, 1, 50]]}] 
kglr
- 403.4k
- 18
- 501
- 959