Purpose: To propose an alternative radiation therapy (RT) planning and delivery scheme with optimal angular beam sampling and intrabeam modulation for improved dose distribution while maintaining high delivery efficiency. Methods: In the proposed approach, coined as dense angularly sampled and sparse intensity modulated RT (DASSIM-RT), a large number of beam angles are used to increase the angular sampling, leading to potentially more conformal dose distributions as compared to conventional IMRT. At the same time, intensity modulation of the incident beams is simplified to eliminate the dispensable segments, compensating the increase in delivery time caused by the increased number of beams and facilitating the plan delivery. In a sense, the proposed approach shifts and transforms, in an optimal fashion, some of the beam segments in conventional IMRT to the added beams. For newly available digital accelerators, the DASSIM-RT delivery can be made very efficient by concatenating the beams so that they can be delivered sequentially without operator's intervention. Different from VMAT, the level of intensity modulation in DASSIS-RT is field specific and optimized to meet the need of each beam direction. Three clinical cases (a head and neck (HN) case, a pancreas case, and a lung case) are used to evaluate the proposed RT scheme. DASSIM-RT, VMAT, and conventional IMRT plans are compared quantitatively in terms of the conformality index (CI) and delivery efficiency. Results: Plan quality improves generally with the number and intensity modulation of the incident beams. For a fixed number of beams or fixed level of intensity modulation, the improvement saturates after the intensity modulation or number of beams reaches to a certain level. An interplay between the two variables is observed and the saturation point depends on the values of both variables. For all the cases studied here, the CI of DASSIM-RT with 15 beams and 5 intensity levels (0.90, 0.79, and 0.84 for the HN, pancreas, and lung cases, respectively) is similar with that of conventional IMRT with seven beams and ten intensity levels (0.88, 0.79, and 0.83) and is higher than that of single-arc VMAT (0.75, 0.75, and 0.82). It is also found that the DASSIM-RT plans generally have better sparing of organs-at-risk than IMRT plans. It is estimated that the dose delivery time of DASSIM-RT with 15 beams and 5 intensity levels is about 4.5, 4.4, and 4.2 min for the HN, pancreas, and lung case, respectively, similar to that of IMRT plans with 7 beams and 10 intensity levels. Conclusion: DASSIS-RT bridges the gap between IMRT and VMAT and allows optimal sampling of angular space and intrabeam modulation, thus it provides improved conformity in dose distributions while maintaining high delivery efficiency.