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Perspectiva vs. perspetiva vs. ponto de vista

The primary difference between perspectiva and perspetiva is spelling based on geography (Brazil vs. Portugal). Both refer to a view, an outlook, or an artistic technique. In contrast, ponto de vista is a phrase equivalent to point of view, largely focusing on specific opinions or stances.

Perspectiva

B2
This is the standard spelling in Brazilian Portuguese. It refers to a mental view, an expectation for the future (an outlook), or the technique of representing 3D objects on a 2D surface. In European Portuguese, this spelling is only used if the speaker audibly pronounces the letter c, which is rare.
As perspectivas econômicas para o próximo ano são ótimas.
(The economic outlooks for next year are great.)
O artista usou a perspectiva para dar profundidade ao quadro.
(The artist used perspective to give depth to the painting.)
Da minha perspectiva, nós tomamos a decisão certa.
(From my perspective, we made the right decision.)
Ela não tem nenhuma perspectiva de crescimento nesta empresa.
(She has no prospect of growth in this company.)

Perspetiva

B2
This is the standard spelling in European Portuguese (Portugal, African Lusophone countries). The silent c is removed in writing. It has the exact same definition as perspectiva: visual depth, mental outlook, or expectation.
É importante analisar o problema numa nova perspetiva.
(It is important to analyze the problem from a new perspective.)
A perspetiva de chuva estragou os nossos planos para o fim de semana.
(The prospect of rain ruined our plans for the weekend.)
Este desenho não tem a perspetiva correta.
(This drawing does not have the correct perspective.)
A tua perspetiva sobre a política é muito interessante.
(Your perspective on politics is very interesting.)

Ponto de vista

B1
Literally translated as point of view. While it can recall a physical angle, it is most commonly used to express a personal opinion, an argument, or a specific way of thinking about a subject. It is slightly less formal than perspectiva.
Eu entendo o seu ponto de vista, mas não concordo.
(I understand your point of view, but I do not agree.)
Sob o ponto de vista médico, o paciente está estável.
(From a medical standpoint, the patient is stable.)
O livro conta a história do ponto de vista do vilão.
(The book tells the story from the villain's point of view.)
Cada pessoa tem um ponto de vista diferente sobre a vida.
(Every person has a different point of view on life.)

Summary

Use perspectiva in Brazil and perspetiva in Portugal; they cover art, mental outlooks, and future expectations. Use ponto de vista when specifically discussing opinions, arguments, or the angle from which a story is told.